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Full text of "Forest mensuration"

FOREST MENSURATION 



C. A. SCHENCK, Ph.D. 

Director Biltmore Forest School, and Fort 
the Biltmore Estate 



MCMV 



THE UNIVERSITY PRESS 
of SEWANEE TENNESSEE 



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FOREST MENSURATION 



By 

C. A. SCHENCK, Ph.D. 

Director Biltmore Forest School, and Forester to 
the Biltmore Estate 



MCMV 



THE UNIVERSITY PRESS 
of SEWANEE TENNESSEE 



Digitized by the Internet Archive 

in 2009 with funding from 

NCSU Libraries 



http://www.archive.org/details/forestmensuratioOOsche 



PREFACE 



Dear Readers : 

In the following pages an attempt is made to treat "Forest Men- 
suration" from a scientific-mathematical standpoint as well as from 
the view point of practical application. 

Naturally, pamphlets of as restricted a character as this treatise on 
forest mensuration address themselves to a very restricted circle of 
readers ; and the expense of printing is never covered by the returns from 
sales. 

Thus it becomes necessary, in order to reduce the expense of pub- 
lication, to omit all, or practically all, lengthy explanation of a mathe- 
matical nature which the teacher at a forest school can easily supply 
in the course of his lectures. 

The present Biltmore pamphlet on Forest Mensuration is intended, 
above all, to assist the students enlisted at the Biltmore School. It con- 
tains the teacher's dictation which the students, in former years, were 
compelled to take down in long or shorthand, to the annoyance of both 
teacher and students. 

It cannot be expected that a present-day lumberman will take a direct 
and personal interest in any of the following paragraphs. Still, in con- 
servative forestry, in destructive forestry, and in any other business en- 
terprise, the truism is worth remembering that "knowledge is the best 
of assets." 

Knowledge certainly forms the only unalienable factor of production. 

With the advent of high stumpage prices, the owner of woodland will 
be inclined to consider, under many circumstances, the advisability of 
forest-husbandry — an idea which was as preposterous in past decades of 
superabundance of timber as the raising of beef cattle, some sixty years 
ago, in the prairies then abounding in buffalo. 

Financially considered, a proper outcome of forest-husbandry is and 
must be based on a proper application of the theories and principles 
involved in forest mensuration. 

I shall be deeply grateful to a kind reader who, discovering mistakes 
or incongruities in the following paragraphs, will take the trouble of 
sending me a timely hint. Most truly, 

C. A. SCHENCK, 

Director Biltmore Forest School, and 
Forester to the Biltmore Estate. 
August i, 1905. 



LECTURES ON FOREST MENSURATION 



SYNOPSIS OF CONTENTS BY PARAGRAPHS. 



Par. 



I. Definition and subdivision. 



Par. 


II. 


Par. 


III. 


Par. 


IV. 


Par. 


V. 


Par. 


VI. 


Par. 


VII. 


Par. 


VIII. 


Par 


IX. 


Par. 


X. 


Par. 


XI. 


Par. 


XII. 


Par. 


XIII. 


Par. 


XIV. 


Par. 


XV. 


Par. 


XVI. 


Par. 


XVII. 


Par. 


XVIII. 


Par. 


XIX 


Par. 


XX. 


Par. 


XXI. 


Par. 


XXII. 


Par. 


XXIII. 


Par. 


XXIV. 


Par. 


XXV. 


Par. 


Si 
XXVI. 


Par. 


XXVII. 


Par. 


XXVIII. 


Par. 


XXIX. 


Par. 


XXX. 


Par. 


XXXI. 


Par. 


XXXII. 


Par. 


XXXIII. 


Par. 


XXXIV. 



CHAPTER I.— VOLUME. 

Section I.— Volume of Trees Cut Down. 

Units of volume. 

Mathematical form of trees. 

Cylinder 

Apollonian Paraboloid. 

Cone. 

Ne ill's paraboloid. 

Riecke's, Huber's and Smalian's formule. 

Hossfeld's formule. 

Simony's formule. 

Sectional measurement. 

Measuring the length of a log. 

Measuring the sectional area. 

Instruments for measuring diameters. 

Units of log measurement in the United States. 

Board-rules. 

Standard-rules. 

Cubic foot-rules. 

Equivalents. 

Xylometric method. 

Hydrostatic method. 

Factors influencing the solid contents of cordwood. 

Reducing factors for cordwood. 

Local peculiarities with reference to stacked wood. 

Bark. 

Section II. — Volume oe Standing Trees. 

Methods of obtaining the volume of standing trees. 

Helps and hints to find the volume of standing trees. 

Scientific methods of ascertaining the cubic contents of 
standing trees by mere measurement. 

Form factor method. 

Kinds of form factors mathematically. 

Kinds of common form factors in European practice. 

Means for exact mensuration of standing trees. 

Measuring the height of a standing tree. 

Factors influencing the exactness of hypsometrical ob- 
servations. 



VI. 



Forest Mensuration 



Par. 


XXXV. 


Par. 


XXXVI. 


Par. 


XXXVII. 


Par. 


XXXVIII 



Indirect mensuration of diameter. 
Pressler's telescope. 
Auxiliaries for calculation. 
Tree volume tables. 



Par. 



XXXIX. 



Par. 


XL. 


Par. 


XLI. 


Par. 


XLII. 


Par. 


XLIII. 


Par. 


XLIV. 


Par. 


XXV. 


Par 


XL VI. 


Par. 


XLVII. 


Par. 


XLVIII. 


Par. 


XLIX, 


Par. 


L. 


Par 


LI. 


Par. 


LII. 


Par. 


LIU. 


Par. 


LIV. 


Par. 


LV. 


Par. 


LVI. 


Par. 


LVII. 


Par. 


LVIII. 


Par. 


LIX. 


Par. 


LX. 


Par. 


LXI. 


Par. 


LXII. 


Par. 


LXIII. 


Par. 


LXIV. 


Par. 


LXV. 


Par. 


LXVI. 


Par. 


LXVII. 


Par. 


LXVIII. 



Section III. — Volume of Forests. 

Synopsis of methods for ascertaining the volume of 

forests. 
Estimation of forest volume. 
Principles underlying the exact mensuration of forest 

volume. 
Field work for exact valuation surveys. 
Basal assumptions. 
Selection of sample trees. 
Draudt-Urich method. 
Robert Hartig method. 
Average sample-tree method. 

Exact mensuration without cutting sample trees. 
Combined measuring and estimating. 
Form factor method. 
Form height method. 
Volume table method. 
Yield table method. 
Distance figure. 

Algon's Universal Volume Tables. 
Schenck's graphic method. 
Factors governing the selection of a method of valuation 

survey 
Factors influencing the selection of sample plots. 
Sir D. Brandis method. 
Pinchot-Graves method on Webb estate. 
The gridironing method. 
Forest reserve methods. 
Sample squares. 
Pisgah Forest method of 1896. 
Pisgah Forest method for stumpage sale, bark sale and 

lumbering operations. 
Henry Gannett's method, adopted for the XHth census. 
A forty method used in Michigan. 
Dr. Fernow's forty method used at Axton. 



CHAPTER II— AGE OF TREES AND OF FORESTS. 

Par. LXIX. Age of trees cut down. 

Par. LXX. Age of standing trees. 

Par. LXXI. Age of a forest. 



Forest Mensuration 



vn. 



Par. 



CHAPTER III.— INCREMENT OF TREES AND OF FORESTS. 

Section I. — Increment of a Tree. 

The kinds of increment. 

Height increment. 

The current height increment. 

The average height increment. 

Relative increment of the height. 

Diameter increment. 

Sectional area increment. 

Relative increment of diameter and of sectional area. 

Volume increment. 

Section analysis. 

Noerdlinger's paper-weight method. 

Schenck's graphic tree analysis. 

Wagener's method and stump analysis. 

Pressler's method. 

Breyman's method. 

Factors influencing the cubic volume increment. 

Volume increment percentage of standing trees. 

Interdependence between cubic increment and increment 

in feet b. m., Doyle. 
Construction of volume tables. 



Par. 


LXXII. 


Par. 


LXXIII. 


Par. 


LXXIV. 


Par. 


LXXV. 


Par. 


LXXVI. 


Par. 


LXXVII. 


Par. 


LXXVIII. 


Par. 


LXXIX. 


Par. 


LXXX. 


Par. 


LXXXI. 


Par. 


LXXXII 


Par 


LXXXIII. 


Par. 


LXXXIV. 


Par. 


LXXXV. 


Par. 


LXXXVI. 


Par. 


LXXXVII. 


Par. 


LXXXVIII. 


Par. 


LXXXIX. 



xc. 



Par. 


XCI. 


Par. 


XCII. 


Par. 


XCIII. 


Par. 


XCIV. 


Par. 


xcv. 


Par. 


XCVI. 


Par. 


XCVII. 


Par. 


XCVIII. 


Par. 


XCIX. 



Section II. — Increment of a Wood. 

Increment of forests. 

Method of construction of normal yield tables. 

Gathering data for normal yield tables. 

Normal yield tables, their purpose and contents abroad. 

Retrospective yield tables. 

Yield tables of the Bureau of Forestry. 

The increment of a woodlot. 

Ascertaining the increment of woodlots by sample trees. 

Current increment ascertained from average increment. 



Par. 
Par. 



CHAPTER IV.— LUMBER. 
C. Units of lumber measure. 
CI. Inspection rules and nomenclature. 



Par. 



CHAPTER V.— STUMPAGE-VALUES. 
CII. Stumnaaie-values. 



FOREST MENSURATION 



PARAGRAPH I. 

DEFINITION AND SUBDIVISION. 

Definition : By "Forest Mensuration," the forester ascertains the vol- 
ume, the age, the increment and the stumpage value of trees, parts of 
trees and aggregates of trees. As a branch of forestry, forest mensura- 
tion may be divided into the following five parts : 

I. Determination of volume of trees cut down, of standing trees 
and of forests. 
II. Determination of age of trees and of forests. 

III. Determination of increment of trees and of forests. 

IV. Determination of sawn lumber. 
V. Determination of stumpage value. 

Circular 445 of the Bureau of Forestry defines mensuration as "the 
determination of the present and future product of the forest." 

American literature is found in Bulletin 20, Division of Forestry; Bul- 
letin 36, Bureau of Forestry ; S. B. Green, page 132 ; Lumber & Log Book 
and Lumberman's Handbook, edited by the "American Lumberman." 



CHAPTER I.— VOLUME. 

SECTION I.— VOLUME OF TREES CUT DOWN. 
PARAGRAPH II. 

UNITS OF VOLUME. 

The volume of a tree or of a tree section is expressed : 

1. For scientific purposes, on the basis of exact measurements, in 

cubic feet or cubic meters. 

2. For practical purposes, by estimates according to local usage, often 

assisted by partial measurement, in local units (feet board 
measure; standards; cords; cubic feet; cord feet; etc.). 

PARAGRAPH III. 

MATHEMATICAL FORM OF TREES. 

Trees do not grow, like crystals, according to purely mathematical laws. 
Tree growth is deeply influenced by individuality, by surroundings, by 
accidental occurrences, etc. 
2 




2 Forest Menstiration 

The body of a tree, considered as a conoid (a solid body formed by 
the revolution of a curve about an axis), is very complicated, being 
formed by a curve of high power. This is the case even in straight and 
clear boled conifers. The tree bole shows, however, in certain sections 
of its body frequently a close resemblance to a truncated neilloid, cylinder, 
paraboloid and cone. 

The longitudinal section of conoids is outlined by a curve correspond- 
ing with the general equation 

y 2 = px« 
in which y is the ordinate (corresponding with the radius of the basal 
area), x the abscissa (representing the height of the conoid), n the 
power of the curve ; whilst p is merely a constant factor. The volume 
v of the conoid is obtained by integral calculus : 

v _ y 2 7tx 
n + 1 

It is equal to sectional area, s, times height, h, over (n-j-i). 

The truncated volumes are developed by deducting a small top conoid 
from a large total conoid. 

Stht — s 2 h 2 

vol. tronc.= 

n + 1 

In the general curve equation 

y 2 = px« 

we find represented : 

A. For n equal to o, the cylinder; 

B. For n equal to i, the Apollonian paraboloid, wherein the ratio 

between sectional area and height is constant ; 

C. For n equal to 2, the cone, wherein the ratio between radius of 

sectional area and height is constant; 

D. For n equal to 3, Neill's paraboloid, the truncated form of which 

is found at the basis of our trees. 

The top of the tree resembles a cone or Neilloid ; the main bole 
resembles the cylinder or the Apollonian paraboloid. 

The cross section (see Par. XIII.) through a tree taken perpen- 
dicular to its axis shows a more or less circular form. Near 
sets of branches and near the roots, however, the outline is 
irregular. The center of the circle usually fails to coincide with 
the axis of the tree. 

PARAGRAPH IV. 

CYLINDER. 

The cubic contents v of a cylinder are equal to the height h of the 
cylinder, multiplied by the sectional area J of the cylinder. 

vol. cylinder = h.s 



sux>\ 



Forest Mensuration 



€ K- 
3 



PARAGRAPH V. 

APOLLONIAN PARABOLOID. 

The volume v of the Apollonian paraboloid is equal to height multi ■ 
plied by Yi sectional area, or equal to ^ of a cylinder having the same 
height and the same basal area. 

h.s 
vol. apol. = - — 

The volume t of the truncated Apollonian paraboloid may be ascer- 
tained as : 

A. Height of trunk times arithmetical mean of top sectional area 

and base sectional area. 

s t + s„ 

t. apol. = h 

2 

B. Height of trunk times sectional area in the midst of the trunk. 

t. apol. = h.sj 



PARAGRAPH VI. 

CONE. 

The volume of the ordinary cone is equal to height of cone times 1/3 
sectional area at the base. 

h.s 
vol. coDe = — 
3 

The volume t of the truncated cone is equal to 1/3 height of trunk 
times sum total of top sectional area si, basal sectional area S2, and V si S2 

h t/ 

t. cone = — (Sj + s 2 + V s 1 s 2 ) 



PARAGRAPH VII. 

NEILL's PARABOLOID. 

The volume of the Neilloid equals Y\ of its height times sectional area 
at the base. 



vol. neil. = 



h.s 



The volume of the truncated neilloid t equals 

t. neil. = — ( s t + s 2 + &&^* [^ s"7+ f s^] J 

wherein h denotes the height of the trunk; Sj and s 2 the top sectional 
area and the basal sectional area of the trunk. 



\{H js\V 



Forest *minsuration 



X 



PARAGRAPH VIII. 
riecke's, huber's and smalian's formule. 

J 

* Formules of practical and scientific application, used here and abroad, 
to ascertain the contents of logs, are those published by Smalian, Riecke 
and Huber. 
^M»^V Riecke's formula holds good for n equal to o, I and 2, and is almost 
correct for the neilloid. 

Smalian over-estimates and Huber under-estimates the actual contents 
of the truncated cone and of the truncated neilloid. 

h 
Riecke — Vol. of trunk = — (Sj + 4s i + s 2) 

6 

Huber — Vol. of trunk = h.sj 

h 
Smalian — Vol. of trunk = — (s t -f- s 2 ) 

Si designates the sectional area in the midst of the trunk, whilst si and S2 
represent basal sectional area and top sectional area. 

PARAGRAPH IX. 

hossfeld's formule. 
The formule given by Hossfeld is : 

h 
Vol. of trunk = — (3 S| + s 2 ) 
4 

It holds good for cylinder, cone and paraboloid. Si designates* the sec- 
tional area at J of the height of the trunk. 

PARAGRAPH X. 

simony's formule. 

Simony's formule requires measurements of sectional areas at J4, *A 
and 24 of the height of the trunk, thus avoiding the irregularities caused 
by the roots at the base and by the branches at the top of a tree-trunk. 

h 
Vol. of trunk = — (2 S| — sj -f 2 S| ) 

This formule holds good for the four standard conoids. 



PARAGRAPH XL 

SECTIONAL measurement. 

The formules given in Paragraphs III. to X. have, in C. A. Schenck's 
opinion, a historic interest only when applied to whole trees. It is much 
safer to ascertain the volume of a tree bole by dissecting it into (imag- 



Forest Mensuration 5 

inary) log sections of equal length, considering each of such sections 
as a cylinder or as a truncated paraboloid. The shorter the length of 
the sections, the greater the accuracy of the result. In scientific research, 
the length of a section varies from 5 feet to 10 feet. Obviously, at the 
top of the bole an uneven length is left, which it might be wise to ascer- 
tain as a cone (or paraboloid — Bulletin 20). The volume of the total 
bole, from stump to tip, equals, if the length of such full section is "\," 
and that of the top cone is "b," and 

1 ) if sectional areas si, S2, S3, s n are measured at the big end of each 

section : 

vol bole =-(s 1 +2s 2 + 2s, + s n ) + -~ 

2) if sectional areas Si,Sn, Sm, s m are measured in the midst of each 

full section, and sectional area s n at the basis of the top cone : 

b.Sn 
vol. bole = 1 (si -f- Sn -f- Sin + s m ) -f 

The former formula is based on Smalian and the latter on Huber. 

In a similar way, and with still greater accuracy, the more complicated 
formulas of Riecke, Hossfeld and Simony might be adapted to sectional 
measurements. 

Remark : If the diameter in the middle of a log is larger than the 
arithmetical mean of the end diameters, then the log contains more vol- 
ume than the truncated cone, and vice versa. 

If the sectional area at the midst of the log is larger than the arith- 
metical mean of the end sectional areas, then the log contains more 
volume than the truncated paraboloid, and vice versa. * 

PARAGRAPH XII. 

MEASURING THE LENGTH OF A LOG. 

The length of a log is measured with tape, stick or axe handle. In 
American logging, logs are usually cut in lengths of even feet, increased 
by an addition of two inches to six inches, which addition allows for 
shrinkage, for season checks, for damage to the log ends inflicted by 
snaking or driving, and for the trimming in the saw mill required to 
removed such end defects. 

In Continental Europe, the standard log lengths are multiples of even 
decimeters. An excess-length of up to eight inches is neglected. 

Crooked logs are made straight by deductions either from the length 
or from the diameter. Crooked trees should be dissected into very shor*- 
logs. 

The standard length of a New England log is 13 feet. 

In the case of big logs, great care must be taken by the sawyers to 
obtain end-cuts perpendicular to the axis of the log. 

The sum of the lengths of logs cut from a tree is termed "used length." 
The total length of that portion of a bole which is merchantable under 
given conditions is called "merchantable length." 



^N**JsJL 



^%> V % f «OA^*^ 



6 Forest Mensuration 

PARAGRAPH XIII. 

MEASURING THE SECTIONAL AREA. 

The sectional areas are ascertained with the help of measuring tape, 
caliper, tree shears, tree compasses, Biltmore measuring stick, etc. 

The sectional area is thus derived from the measurement either of the 
diameter or of the circumference. 

For exact scientific investigations the planimeter or the weight of an 
even-sized piece of paper may be used. 

It is best to consider the sectional area of a tree as an ellipse, the 
surface of which is : 

TV 

surface = — D.d, 
4 

the big diameter D being measured vertically to the small diameter d. 

Usually, however, the average diameter of the tree at a given point 

is found as the arithmetical mean of the big and small diameter at that 

point measured crosswise and not as the square root of the product of 

such diameters. Since 

D + d , 

the average diameter is invariably, though slightly, over-estimated by 
crosswise measurement. Hence it is wise to drop, as an arbitrary offset, 
the excess of fractions of inches over full inches. 

The arithmetical mean of the sectional areas belonging to diameters 
measured crosswise leads to still greater mistakes. 

» 

PARAGRAPH XIV. 

INSTRUMENTS FOR MEASURING DIAMETERS. 

Log calipers are made of pyrus wood or of metal. American make 
(Morley Bros., Saginaw, Mich.) cost $4.00 each. The moving leg of the 
caliper is kept in place by a spring or a screw or a wedge. 

The best European makes are the "Friedrich" and the "Heyer and 
Staudinger." Wimmenauer's "addition-caliper". counts the trees and adds 
their sectional areas automatically. 

Short legged calipers, named "Dachshunds" by C. A. Schenck, can be 
used for trees the radius of which exceeds the length of the legs. The 
diameter is, in that case, indirectly found by the help of the secant joining 
the tips of the legs, which are about 5" long. 

"Tree compasses," opening from six inches to thirty-six inches, and 
made of nickel-plated steel, cost (at Morley Bros.) $7.50. "Tree shears" 
(Treffurth) find the angle formed by the shear-legs when pressed against 
the tree and directly derive therefrom the diameter or the sectional area 
of the tree. 

The "diameter tape" slung around the tree usually yields too large a 
diameter, since the circle embraces the maximum of surface by the min- 
imum of length. 



Forest Mensuration 



The "Biltmore Measuring Stick" can be well used in timber cruising. 
It requires the exact adjustment of distance between eye and fist of ob- 
server (usually 26 inches), and gives directly the diameter at the point 
of the stick where the sight line passes the tree tangentially. The stick 
is held horizontally against the tree. 

26-inch Biltmore Measuring Stick. 



Length on 
the stick. 


Diameter 
with bark. 


Contents of 
butt log. 


Contents of 
two logs. 


Contents of 
three logs. 


2.8" 
5-4" 
7-7" 
9.9" 


3" 
6" 

9" 
12" 


Allowing three inches for bark and 
three inches for taper, per log; assuming 
thst all logs are 14' long. 


1 1.9" 
13-8" 
15.6" 
17.3" 


15" 
18" 
21" 
24" 


22 ft. b. m. 

56 " " 
106 " " 
171 " " 


29 ft. b. m. 

78 " " 
162 " " 

277 " " 


39 ft. b. m. 
85 " " 
184 " " 

333 " " 


18.9" 
20.4" 
21.9" 
23.3" 


27" 
30" 

33" 
36" 


253 " " 
350 *' " 
463 " " 

591 " " 


424 " 
603 " " 
813 " " 
1054 " " 


530 " 

774 " 
1066 " " 
1404 " " 



Mr. Snead recommends to measure the circumference outside the bark 
at the big end and to divide the result by 4. He claims that the quotient 
yields the diameter at the small end inside bark in such a way as to offset 
mistakes made by Doyle, who under-estimates small logs and over-esti- 
mates big logs. Snead's suggestion is good, provided, that the cross sec- 
tion of the log is fairly circular, and that the difference between the small 
diameter inside bark at the small end and the big diameter outside bark 
at the big end, amounts to about 7 inches. 



Diameter at small end 
inside bark. 



10 inches. 

15 
20 

25 

30 

35 



Contents of 16 foot logs, in feet b.m. 



Doyle. 


Snead. 


Actual saw cut. 


36' 


8i' 


70' 


121' 


169' 


157' 


256' 


289' 


279' 


441' 


441' 


436' 


676' 


625' 


628' 


961' 


841' 


856' 



The multiples of sectional area (derived from the diameter in inches, 
but expressed in square feet) by length of log are readily obtained from 
cylinder tables published by various authors. The log scale or log rule 
used by the lumbermen (Lufkin rule) gives at a glance the contents of 
logs 8 to 20 feet long, according to their diameter. 



8 Forest Mensuration 

PARAGRAPH XV. 

UNITS OF LOG MEASUREMENT IN THE UNITED STATES. 

The units of log measurement used in the United States differ greatly. 
Graves' Handbook gives 43 "rules." The rules can be subdivided into 
three main grops : 

Board feet group (Par. XVI.) ; 
Standard log group (Par. XVII.) ; 
Artificial cubic foot group (Par. XVIII. ). 

PARAGRAPH XVI. 

BOARD-RULES. 

A foot board measure is a superficial foot one inch thick, in boards one 
inch or more in thickness. It is a superficial foot, irrespective of thick- 
ness, in boards less than one inch in thickness. 

The "board rules" merely guess at the number of feet board measure 
obtainable from logs of a given diameter. The guess is based upon 
either graphical considerations, circles of specified diameters being sub- 
divided into parallelograms 1% inch thick (diagram method), or else 
on mathematical considerations, with a view to the fact that a cubic foot 
of timber should theoretically yield 12 board feet of lumber, whilst the 
actual loss for slab, saw kerf, etc., will reduce the output by 30% to 
50%. In the Biltmore band saw mill, by over one thousand tests, the 
actual loss for logs 12 inches to 40 inches in diameter has been found to 
amount to 30%, or close to 1/3. Consequently, it is safe to say that the 
band saw obtains from a cubic foot of log 8 board feet of lumber. * 

The number of board feet which a log actually yields depends on: 

1. The actual cubic volume of a cylinder having the length and small- 
est diameter inside bark of the log. 

2. The defects of the log (heart rot, wind shake, bad knots, crooks), 
which are usually eliminated by edger or trimmer. 

3. The gauge of the saw, on which the saw kerf depends. The kerf 
of band saws amounts to Y% inch, of circular saws to usually *4 inch, of 
inserted tooth saws (of large diameter) to y% inch, of resaws to 1/16 
inch. 

4. The exactness of the work, especially depending on trueness of saw, 
proper lining of saw and sawyer's skill ; further, on the exactness of the 
setworks. 

5. The thickness of boards obtained ; the minimum width of boards 
permitted ; the amount of lumber wasted in the slabs ; shrinkage in drying. 

The following table compares the contents of logs in cubic feet with 
their contents in feet board measure as found by C. A. Schenck through 
a thousand tests of actual yield in yellow poplar, as given by Doyle's 
rule and by Lumberman's Favorite rule. 

The figures given in columns c, f and i show the contents of a 
log in feet board measure after Schenck's findings, Doyle's and Favorite 



Forest Mensuration 



9 



rules. They are converted into cubic feet (columns d, g, and j) by divid- 
ing by 12. The loss incurred in sawing is shown by percentages (col- 
umns e, h, k) representing the ratio between the actual cubic con- 
tents of a log (as given in column b), and the cubic contents of inch 
boards (columns d, g, j) obtained from such log. 

It will be observed that the loss in the actual yield according to Schenck 
forms a nearly constant proportion of the cubic contents of a log in the 
case of all diameters, whilst, according to Doyle's and Favorite rules, the 
figures of loss vary greatly. 

The table refers to logs 12' long sawed into i-inch boards. 



Diameter 


Contents. 
Cubic 


Schenck. 


Doyle. 


Favorite. 


of 




















Log. 


Feet. 


Feet 


Cubic 


Loss 


Feet 


Cubic 


Loss 


Feet 


Cubic 


Loss 


Inches. 




b. m. 


Feet. 


0/ 

/o 


b. m. 


Feet. 


% 


b. m. 


Feet. 


% 


a. 


b. 


c. 


d. 


e. 


f. 


g- 


h. 


i. 


j- 


k. 


8 


4-2 

53 

6-5 
8.0 








12 


0.9 
1.6 


76 








9 
10 








19 

27 


70 














2.3 
4.0 


65 
61 








1 1 








37 
48 








12 


9-4 


78 


6-5 


31 


57 


49 


4-i 


56 


13 


11 .0 


96 


S.o 


27 


61 


5-i 


54 


62 


5-2 


53 


14 


12.8 


112 


9-3 


27 


75 


6-3 


5i 


74 


6.2 


52 


15 


14-7 


129 


10.7 


27 


9i 


7.6 


48 


90 


7-5 


49 


16 


16.8 


146 


12. 2 


27 


108 


9.0 


46 


107 


8.9 


46 


17 


18.9 


162 


13-5 


29 


127 


10.6 


44 


125 


10.4 


45 


iS 


21 .2 


1 So 


15.0 


29 


147 


12.3 


42 


148 


12.3 


42 


19 


23.6 


197 


16.4 


30 


169 


14. 1 


40 


170 


14.2 


39 


20 


26.2 


212 


17-7 


32 


192 


16.0 


39 


186 


15-5 


41 


21 


28.9 


230 


19.2 


34 


217 


18. 1 


37 


214 


17.8 


38 


22 


3i -7 


248 


20.7 


35 


243 


20.3 


36 


243 


20.3 


36 


23 


34-6 


266 


22. 2 


36 


271 


22.6 


35 


268 


22.3 


36 


24 


37-7 


298 


24.8 


34 


300 


25.0 


33 


294 


24- 5 


35 


25 


40.9 


33i 


27.6 


32 


33i 


27.6 


32 


326 


27.2 


33 


26 


44-2 


362 


30.2 


32 


363 


303 


3i 


35S 


29. S 


33 


27 


47-7 


394 


32-9 


3i 


397 


33- 1 


30 


390 


32.5 


32 


28 


51-3 


422 


35-2 


3i 


432 


36.0 


30 


422 


35-2 


3i 


29 


55-0 


456 


38.0 


3i 


469 


39- 1 


29 


44S 


37-3 


32 


30 


58.9 


488 


40.7 


3 1 


507 


42-3 


28 


474 


39-5 


33 


3i 


62.9 


5i8 


43-2 


3i 


547 


45-6 


27 


509 


42.4 


33 


32 


67.0 


556 


46.3 


3i 


588 


49.0 


27 


544 


45-3 


32 


33 


71-3 


596 


49-7 


30 


631 


52.6 


26 


5S9 


49.1 


3i 


34 


75-7 


634 


52.8 


30 


675 


56.3 


26 


634 


52.8 


30 


35 


80.2 


670 


55-8 


30 


721 


60. 1 


25 


662 


55-2 


3i 


36 


84.8 


710 


59-2 


30 


768 


64.0 


25 


690 


57-5 


32 


37 


89.6 


755 


62.9 


30 


817 


68.1 


24 


734 


61 .2 


32 


38 


94-5 


S06 


66.7 


29 


867 


72.3 


23 


778 


64.8 


3i 


39 


99-5 


850 


70.8 


29 


910 


75-8 


24 


824 


68.7 


3i 


40 


104.7 


901 


75-0 


28 


972 


81.0 


23 


870 


72.5 


3i 



From column e it is evident that the bandsaw wastes close to 1/3 
of the cubic contents of a cylindrical log, or 4' b. m. out of every cubic 
foot. 

Consequently, from hardwood logs 12 feet to 16 feet long, the band- 



io Forest Mensuration 

saw will obtain the following actual number of feet b. m. (in 4/4" 
thickness) : 

D 2 X 0.78 X 12 X 8 
(a) from 12 foot logs: , almost equal to D 2 X-5 





144 


D 2 


X 0.78 X 14 X 8 




144 


W 


X 0.78 X 16 X 8 




(c) from 16 foot logs: , almost equal to D 2 X-7 

144 

Hence it can be stated generally, for logs of medium length "L," that 
their contents in band-sawed inch lumber approximate 

D 2 L — 2 

— X feet b. m. 

10 2 

PARAGRAPH XVII. 

STANDARD RULES. 

_ Yv.M The standard rules do not estimate the contents of a log according to 

output in board feet, but compare the log with a local average log. Such 
average logs used to have, in the Northeast, formerly, a diameter of 
either 19 inches (Adirondacks) or 22 inches (Saranac River) or 24 
inches, and were in all cases 13 feet long. 

The 19 inch standard log rule is known as Dimick's rule. Here the 

"standard" or "market" is a log 13 feet long and 19 inches thick. On a 

"b<\v, o-i i.*f 22 jnch base ft j s T ^ f ee t long and 22 inches thick. On a 24 inch base 

*"! <^ it is 13 feet long and 24 inches thick. 

\ The standard contents of a given log are found by dividing the cubic 

'volume of the standard log into the cubic volume of the given log. 

d 2 X h 

v (in standards) equals: 

19 3 X 13 

Scientifically and mathematically the standard rules are superior to 
the board rules. One market, at a 19 inch base, is generally considered 
equivalent to 200 board feet ; at a 22 inch base, to 250 board feet ; at a 
24 inch base, to 300 board feet. 

It is easily shown that the output of small logs is not as badly under- 
estimated, and the output of big logs not as badly over-estimated on the 
basis of standard rules, as is the case when Doyle's rule alone is applied. 

PARAGRAPH XVIII. 

CUBIC FOOT-RULES. 

In a third group of rules, a new unit, the "artificial cubic foot," is 
introduced. This group of rules is established by law in Maine and New 
Hampshire. (See Graves' Handbook, page 45.) 



Forest Mensuration II 

The artificial cubic foot corresponds with a log 12 inches long and 
16 inches thick, which naturally contains 1.4 cubic feet. The rule as- 
sumes that 40/140 or 28.5% of a log goes to waste in the sawing process 
as dust or slab. 

To quickly transform artificial cubic feet into board feet, the laws pre- 
scribe certain arbitrary equivalents, instead of allowing 12 board feet 
to equal one artificial cubic foot of timber. In New Hampshire, 10 board 
feet equal one artificial cubic foot. In Maine, 11.5 board feet equal one 
cubic foot. The rules might be used in connection with a cylinder table, 
deducting 28.5% from the table data and multiplying the remainder by 
10 or by 11. 5. 

Remark : According to the Forest Reserve Manual, logs over 24 feet 
long are treated as 16 foot logs and fractions thereof. 



PARAGRAPH XIX. 

EQUIVALENTS. 

One cubic meter equals 35.316 feet or 1.308 cubic yards. 

1,000 board feet of sawn lumber, 1 inch and more thick, correspond 
with 2.36 cubic meters of sawn lumber. 

A product of one cubic meter per hectar (2^2 acres) equals a product 
of 14 cubic feet per acre. 

One gallon equals 231 cubic inches in liquid measure, or 268.8 cubic 
inches in dry measure (which is also l /2 peck). 

One liter equals 1.0567 quarts; one cubic foot equals 74805 gallons 
or 28.3 liters. 

Logs yielding when split one cord of wood, will yield, when sawn: 



For log diameter: 


Feet board measure: 


20" 
25" 
30" 
35" 
40" 


515' 
566' 
605' 
629' 
649' 



The Forest Reserve Manual adopts 2 cords as equivalent to 1,000 
feet b. m., provided that the wood is split from timber 10 inches in diam- 
eter and over. 



12 Forest Mensuration 

Table Showing Relative Contents of Logs Without Bark. 



Log diameter. 



i cubic foot equals ft. b. m. Doyle 

i cubic meter per nectar corre- 
sponds with ft. b.m. Doyle per 
acre : 

i cubic meter of log yields ft. b. 
m. Doyle: 

iooo ft. b. m. Doyle equal cubic 
ft: _. 

iooo ft. b. m. Doyle equal cubic 
meters ! . . . 

Artificial cubic feet per i ft. of log 

No. of legal N. H. feet b. m. per 
i ft of log : 

Ft. b. m. Doyle per i ft. of log. . . 



44.8 

787.4 



4.12 



57-68 


86. 


145-5 


218. 


242.7 


161. 


6.87 
•4 


4- 


4- 

2-3 


9- 

7- 



15' 



6.2 



7-3 

102.2 

258.8 

1364 

3.86 
1.56 

156 
16. 



25 



8.09 

113.26 

285.7 
123.6 

3-5 
2-45 

24-5 
27-5 



30' 



8.64 



303 
116 



PARAGRAPH XX. 



XYLOMETRIC METHOD. 



The so-called "physical methods," by which the volume of a (partic- 
ularly irregular) piece of a tree may be accurately found, require either 
the submersion of the piece in water (xylometric method) or the weigh- 
ing of the piece after finding its specific gravity (hydrostatic method, 
§XXL). 

The xylometric method can be applied in three ways, thus : 

0. Submerge the wood in a graded cylinder partly filled with water 
and find the water level before and after submersion. 

b. Submerge the wood in a barrel partly filled with water; dip out 
the water with a gallon measure until the water is as low as it was before 
submersion. The number of gallons dipped out equals the volume of 
the wood submerged. One gallon equals 231 cubic inches. 

c. Place a piece of wood in an empty barrel of known contents ; fill 
to the rim with water by the gallon. The difference between the known 
contents and the number of gallons required gives the quantity of wood 
in gallons. 

In a, b and c it is necessary to use wood dry on the outside, to leave 
the wood in the water a short time only, and to stir it up while in the 
water so as to remove air bubbles. 



PARAGRAPH XXI. 

HYDROSTATIC METHOD. 



The hydrostatic method deals with specific gravities. Specific gravity 
is weight of an object divided by the weight of an equal volume of 



Forest Mensuration 



13 



water. In the metric system, it equals weight in kilograms over cube- 
decimeters of volume. The specific gravity is found by weighing a given 
body, and then weighing it again immersed in water. It equals weight 
outside water over loss of weight submerged in water. The division of 
the metric weight of a large body by the specfic gravity of a sample piece 
yields the volume of the body in cubic decimeters. 

Since wood is lighter than water, usually, a piece of lead must be 
attached to the wood in order to submerge it. There must be ascer- 
tained : 

1. The absolute weight of the piece of lead, H; 

2. The weight of the same piece submerged in water, h ; 

3. The absolute weight of the wood and of the lead, G; 

4. The weight of wood and lead submerged in water, g. 

The weight of the wood alone is, consequently, (G — H). 
The specific gravity of the wood is 

G — H 

S ~(G-g)-(H-h) 

The volume, in cubic feet, of a quantity of wood weighing n pounds, 
and having the specific gravity s, is 

n 1 16n 

volume = — X — = 

s 63 1000s 

The figure 63 represents the weight in pounds of one cubic foot of 
water. 

The specific gravity of wood is greatest close to the stump and in the 
branches. For some species the outer layers show the greatest specific 
gravity; for others the inner layers. 



Species. 


Spec, gravity, 
air dry. 


Weight of lumber per 
1000 ft. b. m. in lbs. 


Weight of one 
cord in lbs. 


White oak 

Beech 

Hard maple .... 
Yellow pine .... 

Spruce 

White pine 


•75 
•7i 
.66 
•52 
•45 
•39 


3900 
3692 
3432 
2704 
2340 
2028 


3985 
3767 
35io 
2761 
2391 
2069 



Rules to convert specific gravity into weight per 1,000 feet board 
measure or into weight per cord read as follows : 

1. Multiply specific gravity by 5,200. The result is the weight of 
lumber per 1,000 feet board measure in pounds. 

2. Multiply specific gravity by percentage of solid wood contained in 
a stacked pile; then multiply the product by 8,050. The result gives the 
weight per cord in pounds. 




14 Forest Mensuration 

FAllSXAPH XXII. 

FACTORS INFLUENCING THE SOLID CONTENTS OF CORDWOOD. 

>v The solid contents of wood stacks depend on the size and the form of 

^r ^- the pieces composing them and on the method of piling. The solid con- 

<v. tents of a cord can be found only by the methods described in Para- 

graphs XX. and XXI. The European experiment stations have collected 
"•^^V^^^^^data to that end on a very large scale, and have established the following 
.-^p^ laws : 

^-^Vvaav^-^ a. The bigger the pieces of wood in a stack, the larger are the solid 
_vv^^^-~^-~~ contents of the stack. 

X»~- ^m^avtj-^j^ £. The longer the pieces of wood, the smaller are the solid contents 
of the stack. 



' c. Pieces piled parallel and tightly greatly increase the solid contents 
of the stack. 

d. During the drying process, hardwoods shrink approximately by 
<s^J_^^^ 12%, and soft woods by 9%. The shrinkage is partly offset by the 
n ^ cracking of wood. 

These rules are important in the pulp, tanningwood and firewood trade. 
PARAGRAPH XXIII. 

REDUCING FACTORS FOR CORDWOOD. 

The countries using the metric system pile wood in space cubic meters. 
One space cubic meter equals .274 cord. The pieces contained "therein 
are 3.28 feet long. For such conditions the following figures hold good : 

a. First class split wood, obtained from sound pieces 12 inches in 
diameter, contains per cord 102.4 cubic feet of solid wood (reducing fac- 
tor 80%). 

b. Composed of inferior split wood, obtained from round pieces having 
a diameter of 6 inches, a cord contains 96 cubic feet of solid wood (re- 
ducing factor 75%). 

c. In heavy, round branch wood (diameters of about 6^ inches) 
87 cubic feet of solid wood are found in a cord (reducing factor 68%). 

d. In round pieces of branch wood, 4 inches in diameter, yy cubic 
feet are found in a cord (reducing factor 60%). 

e. In faggots, 25 to 51 cubic feet make a cord (reducing factor 20% 
to 40%). 

The percentages for broad leafed species are smaller than those for 
conifers, owing to the latter's straight growth. 

At Biltmore, one cord of 8 foot split oak contains about 80 cubic feet ; 
one cord of kindling finely split about 90 cubic feet; one cord of blocks 
12 inches long about 100 cubic feet of solid wood. 



Forest Mensuration 15 

In the sale of tannin wood it is well to sell 5 foot sticks finely split 
rather than heavy blocks 4 feet long. 

In the sale of pulp wood, 12 foot sticks yield much higher returns than 
4 foot sticks, if sales are made by the cord. 



PARAGRAPH XXIV. 

LOCAL PECULIARITIES WITH REFERENCE TO STACKED WOOD. 

Tannin and pulp wood industries sometimes figure at a cord containing 
160 stacked cubic feet, equal to \V\ ordinary cords of 128 stacked cubic 
feet. 

After Graves (page 65), a cord of firewood is in certain sections under- 
stood to be 5 feet long, 4 feet high and 6^2 feet wide. 

Under "a cord foot" is understood a stack 1 foot by 4 feet by 4 feet 
(% cord or 16 stacked cubic feet). 

Under "a cylindrical foot" is understood a stacked cubic foot equal 
to 1/128 cord. The number of such feet (a misnomer for stacked cubic 
feet) in a stick is 

d*Xl 
144 

(/ equals length of stick in feet; d equals its diameter in inches). 

In New England, a cord of pulp wood is sometimes measured by 
calipering the round sticks composing it, and tables are constructed to 
facilitate calculation. Proceed as follows : 

Ascertain diameter of sticks in inches, square them singly, total the 
results and divide by 144. Multiply the quotient by length of sticks in 
feet and divide by 128. 



PARAGRAPH XXV. 

BARK. 

Bark is usually sold and bought by the cord. The tanneries, however, 
instead of measuring a cord of 128 cubic feet, apply the misnomer "one 
cord" to a weight of 2,240 lbs. (the long or European ton). 

Twelve cords of bark fill one common (old) freight car. 

A stack of bark contains from 30% to 40% solid bark. The specific 
gravity of fresh oak bark is 0.874; dried, it is 0.764. 

The bark of white oak has been found (at Biltmore), to comprise: 

In trees 20 years old, 55% of the wood, or 35% of the whole bole ; 
In trees 60 years old, 41% of the wood or 28% of the whole bole; 
In trees 100 years old, 29% of the wood or 22% of the whole bole ; 
In trees 140 years old, 21% of the wood or 17% of the whole bole. 



i6 



Forest Mensuration 



Chestnut oak peeled at Biltmore yields the following results per tree, 
arranged according to the diameter of the trees 4 l / 2 feet above ground: 



Diameter of tree 


Dry Bark in 


Kilogram = r ^^ cord, per Tree. 


chest high in inches. 










Minimum 


Average. 


Maximum. 


6 


5 


13 


27 


7 


6 


17 


36 


8 


8 


24 


48 


9 


12 


33 


61 


IO 


18 


45 


77 


ii 


26 


60 


95 


12 


37 


73 


114 


13 


50 


88 


135 


14 


65 


105 


158 


15 


81 


126 


180 


16 


98 


150 


204 


17 


116 


172 


234 


18 


136 


195 


266 


19 


159 


224 


3H 


20 


181 


250 


365 


21 


205 


275 




22 


230 


305 




23 


265 


336 




24 


275 


375 





If the percentage of bark in a log or tree (scaled with the bark) is 
p, then the bark percentage in ratio to the solid wood alone is : 

100 X p 
100 — p 

According to thickness of bark and diameter of logs, the following 
percentages can be given for the ratio : 

bark 
bark plus timber 



Diameter with 


Thickness of bark. 


bark — inches. 


\" 


1" 


1 4" 


2" 


10 

15 
20 

25 
30 


19% 

12% 

9% 

7% 

6% 


36% 
24% 
19% 
15% 
12% 


51% 
36% 
27% 
22% 
19% 


64% 
46 % 
36% 
29% 
24% 



Forest Mensuration 17 



SECTION II.— VOLUME OF STANDING TREES. 
PARAGRAPH XXVI. 

METHODS OF OBTAINING THE VOLUME OF STANDING TREES. 

The volume of standing trees may be ascertained 

By estimating it (Par. XXVII.) ; 

By measuring heights and diameters (Par. XXVIII.) ; 
By the form factor method, which combines estimates and meas- 
urements (Par. XXIX. f. f.). 

By these means can be obtained the volume of the bole (from roots to 
top bud), or the volume of saw timber in any of the 43 log scales, or 
the volume of firewood in cords, etc., or the total volume, including brush 
and roots. 

Under "used volume,"' Circular 445 of the United States Bureau of For- 
estry understands the sum of the volumes of logs cut from a tree ; under 
"merchantable volume" the total volume of that portion of the tree which 
is merchantable under certain conditions. 

PARAGRAPH XXVII. 

HELPS AND HINTS TO FIND THE VOLUME OF STANDING TREES. 

It is difficult to estimate the cubic contents, wood contents or lumber 
contents of a standing tree. In the case of estimates in board feet, the 
result depends on the exclusion or inclusion of crooked and defective 
pieces, on the taper of the bole, on the soundness of the heart, and on 
the minimum diameter admissible in the top log. Compare end of Par- 
agraph XXXII. 

Most hazardous is the volume estimate of over-aged trees, especially 
in the case of hardwoods (chestnut). 

The following helps might guide the novice : 

1. The volume of a sound tree bole, in cubic meters, is equal to 

1000 
for example, diameter (breast high) 30 c. m. ; contents 0.9 cubic meters. 

2. The contents of a standing tree, in cubic feet, are about 

10 
for example, diameter (breast high), 25 inches; contents (from butt to 
tip), 125 cubic feet. 

3. The number of feet Doyle in a tall sound tree equal 

3 

— D 2 
2 



1 8 Forest Mensuration 

for example, diameter (breast high), 20 inches; contents 600 feet board 
measure. 

4. The contents of a tree in feet Doyle approximate, assuming that 
the bole is cut into 16 foot logs, and that the tree tapers 2 inches per log : 

N X D (D— 12) 

wherein N represents the number of logs obtainable; D the diameter of 
the butt log without bark at breast height. 

5. The cordwood contained in a sound bole is : 

D 2 



X C 
1000 



wherein C amounts to : 



1.5 in the case of trees 8" through ; 
2.0 in the case of trees 16" through ; 
2.5 in the case of trees 24" through. 



PARAGRAPH XXVIII. 

SCIENTIFIC METHODS OF ASCERTAINING THE CUBIC CONTENTS OF STANDING 
TREES BY MERE MEASUREMENT. 

The cubic volume of the bole, on the basis of diameter measurement 
and height measurement, in the case of a standing tree, may (with the 
help of climbing iron, ladders, camera or instruments constructed for 
the purpose) be figured out: ► . 

1. According to the formulas of Hossfeldt, Riecke and Simony. In 
this case, the upper diameters must be measured indirectly. 

2. According to Huber's and Smalian's formulas, the diameters of 
equal sections of the trees being indirectly measured. 

3. According to Pressler's formula, which is, for the volume of the 
bole lying between chest height and top bud, 2/3 of sectional area "S" 
at chest height times "rectified" height of bole. The rectified height "r" 
is the distance of chest height from that point of the tree bole which 
has l / 2 of the chest height diameter (from the "guide point"). The 
equation 2/3 r x S holds good for paraboloid, cone and, at a slight mis- 
take, for the neilloid. 

The volume of that part of the tree bole which lies below chest height 
is ascertained (as a cylinder) as being equal to sectional area chest high 
times 4.5. 

Remark : 4.3' is the chest height usually recognized by the authors ; 
Pinchot adopts 4.5'. 
The Pressler formula does not hold good for truncated boles. 



Forest Mensuration 19 

PARAGRAPH XXIX. 

FORM FACTOR METHOD. 

The form factor or form figure method relies on the measurement of 
the sectional area — usually the one at breast height, — the measurement 
or the estimation of the total height and the estimation of the form 
figure. 

The form factor is a fraction expressing the relation between the actual 
contents of a tree, in any unit, and the ideal contents which a tree would 
have if it were carrying its girth (like a cylinder) up to the top bud 
undiminished. 

The form factor may be given in reference to the volume of the entire 
tree, inclusive of branches in cubic feet ; or in reference to the volume 
of the bole only ; or in reference to the merchantable part of the bole ; 
in the latter case either in feet board measure or in standards or in cords. 

Historic Remarks : Some of the older authors on mensuration saw in 

the cone and not in the cylinder the ideal form of the tree, basing their 

s X h 
form factors on the ideal volume . 



PARAGRAPH XXX. 

KINDS OF FORM FACTORS MATHEMATICALLY. 

Scientifically we distinguish between : 

1. The absolute form factors which have reference only to the volume 
standing above chest height. They can be readily ascertained with the 
help of Pressler's formula. Generally speaking, V equals Sx H x F. 

After Pressler, V equals S x 2/3 x r; thus *— equals F. 

H 
For the cone the absolute form factor is one-third ; for the neilloid 
one-fourth ; for the paraboloid one-half, whatever the height of the tree 
may be. Hans Rienicker, the author of these form factors, finds for 
trees up to 50 years old a form figure of 35% to 43% (in regular, dense 
German woods); in trees 50 to 100 years old, F increases up to 50%; 
thereafter occurs a slight decrease below 50%. 

2. The normal form factors which were recommended by Smalian, 
Pressler and other old-time authors. They have reference to the entire 
volume and necessitate the measurement of the diameter at a given frac- 
tion (usually 1/20) of the total height of the tree. Frequently, in case 
of tall trees, the point of measurement cannot be reached from the ground. 
The bole form factor for diameters measured at 1/20 of the height is : 
For a paraboloid, 0.526 ; for a cone, 0.369 ; for a neilloid, 0.292. These 
form factors, like the absolute form factors, are independent of the height. 

3. The so-called "common form factors" which do not express, as a 
matter of fact, the form of the tree, since they do not bear any direct 
ratio to the degree of the tree curve. They should be termed, more 



20 



Forest Mensuration 



properly, "reducing factors." These form factors alone are nowadays 
practically used. They are based on diameter measurements, chest high, 
and have reference not merely to the bole of the tree, but as well to any 
parts of the bole, to root and branch wood, to saw logs, etc. These form 
factors depend entirely on the height. If, for instance, a paraboloid is 
one rod high, the form factor is 0.673 ; and if it is 8 rods high, the form 
factor is 0.517. 



PARAGRAPH XXXI. 

KINDS OF COMMON FORM FACTORS IN EUROPEAN PRACTICE. 

The following kinds of form factors may be distinguished : 

1. Tree form factors. The tree is considered as bole plus branches. 

2. Timber form factors. The term timber, in Europe, includes all 
parts of the tree having over 3 inches diameter at the small end. 

3. Bole form factors. Bole is the central stem from soil to top bud. 
For America, form factors would be of great value ascertained by exact 
measurements and arranged according to diameter, height and smallest 
log diameter used. 

Tables of form factors may be constructed, for instance, for shortleaf 
pine, on the basis of Olmsted's working plan, pages 17-33. 

PlNUS ECHINATA. 



Diameter. 


Merchantable length 


Cubic feet 


Form fig. 


Contents 




of bole. 


Ideal cylinder. 




b. m. Doyle. 


16" 


36' 


50.3 


3-6 


* 180' 


18" 


47' 


83 


1 


3 


6 


300' 


20" 


5i' 


112 


1 


4 





440' 


22" 


56' 


147 


8 


4 





600' 


24" 


59' 


185 


3 


4 


2 


780' 


26" 


61' 


224 


9 


4 


4 


980' 


28" 


62' 


263 


1 


4 


5 


1 190' 


3o" 


62' 6" 


306 


7 


4 


6 


1420' 


32" 


63' 


35i 


8 


4 


7 


1680' 


34" 


63' 6" 


400 


3 


4 


8 


1930' 


36" 


64' 


457 


3 


4 


9 


2200' 



The influence of age, soil, density of stand, height, diameter and 
species on the various form factors, with cubic measure as a basis, has 
not been fully ascertained. 

For the tree form factor, the most important influence, in the case of 
trees less than 150 years old and raised in a close stand, seems to be 
that of the height of the tree ; with increasing height the tree form factor 
decreases — c. g., for Yellow Pine : 

One pole high 93 

Two poles high 65 

Four poles high 53 

Six poles high 49 



Forest Mensuration 21 

The timber form factor, based on cubic measure of a tree, rises with 
increasing age and increasing height up to a certain point (for Yellow 
Pine at 3 poles), provided that the term timber includes all stuff over 
3 inches in diameter. The timber form factor is a function more of 
the diameter than of the height. Timber form factors of Yellow Pine 
are : 

Trees 1 pole high 07 



Trees 2 poles high 

Trees 3 poles high 

Trees 4 poles high 

Trees 7 poles high 



The timber form factor in shade bearers is a little higher than that 
in light demanders (within an age limit of 150 years, for trees in close 
stand). 

The bole form factor can be found, in fact, only for species forming 
a straight bole free from large branches (hence especially for conifers). 
The bole form factors, to begin with, are large ; with increasing height, 
they decrease gradually to a par with the timber form factors — e. g., for 
Yellow Pine : 

1 pole high 70 3 poles high 49 

2 poles high 55 4 poles high 47 

7 poles high 45 

European common form factors are collected by thousands of measure- 
ments taken in a large variety of localities. It must be remembered that 
a form factor read from a table is never applicable to an individual tree, 
and is only applicable to an average tree amongst thousands. 

For trees less than 120 years old, the branch wood (stuff less than 3 
inches in diameter) comprises from 15% to 28% of the entire tree vol- 
ume; this figure, in the case of broadleaved species, rises from 25% up 
to 33%. For trees as now logged in America, the branchwood percentage 
is naturally very much smaller. 

The tree form factor equals stump plus bole plus branches 

ideal cylinder 

The timber form factor equals all stuff having over 3" diameter 

ideal cylinder 

The bole form factor equals bole from ground to tip 

ideal cylinder 

By form height is meant the product of height (total height of tree) 
times form factor, or else that much of the height of the ideal cylinder 
which the tree volume, poured into the ideal cylinder, would fill. Since 
the form factor on the whole decreases with increasing height, the form 
height is a fairly constant quantity; at least for trees of merchantable 
size. Hence the helps and hints given in Paragraph XXVII (to quickly 
find the volume of standing trees from mere diameter-measurement) may 



22 Forest Mensuration 

% 

lay claim to correctness in many cases. For instance : The cubic con- 
tents of a tree are supposed to be equal to 

tt D 2 X H X F 
X ■ 

4 144 

After Paragraph XXVIL, 2, these contents are also 

2 
—X D 2 

10 

B- 

= D 2 X 78 X H X F 

5 

288 
H X F = =37 

7.8 

As a matter of fact, the form height of trees I foot to 2 feet in diam- 
eter is close to 2>7- And for such trees the equation holds good. 

The form height may also be defined as "volume (standards, cords, 
bark, etc.) per square foot of sectional area chest-high." 

PARAGRAPH XXXII. 

MEANS FOR EXACT MENSURATION OF STANDING TREES. 

The means used to find the exact solid volume of standing trees are 
instruments for measuring the total height of the merchantable length 
of a tree ; instruments for measuring the diameter at given heights ; fur- 
ther tables based on scientific research and experience, or tables merely 
meant to facilitate calculation. Instruments for measuring diameters far 
above ground are needed for the use of the formulas given by Riecke, 
Hossfeldt, Pressler, etc. 

The six paragraphs following next dwell upon these topics. 

PARAGRAPH XXXIII. 

MEASURING THE HEIGHT OF A STANDING TREE. 

The height of a tree can be measured by comparing its shadow with 
the shadow of a stick, say io feet long. The "Lumber and Log Book" 
gives another old method (page 133) of height measurement. If the 
observer places himself in such a way that a small pole stands between 
him and the tree at a distance e, and if he marks on the pole two points 
where his sight, directed towards the top and base of the tree, touches 
the small pole, and if he further ascertains the distance E separating him 
from the tree, then the height of the tree H equals 

E 

— X h 

e 

wherein h represents the number of feet between the two points marked 
on the pole. 



Forest Mensuration 23 

I 

Instruments (hypsometers) for height measuring are sold in many 
forms. The following are frequently used: Rudnicka's instrument; Press- 
or's "Measuring Jack;" Faustmann's "Mirror Hypsometer;" Weise's Tel- 
escope ; Kcenig's "Measuring Board ;" Brandis' "Clinometer ;" Klausner's 
instrument ; Christen's "Non plus ultra." 

Compare Woodman's Handbook, pages 136 to 137, for staff method; 
page 138 for Faustmann's; page 140 for tangential clinometer; page 143 
for mirror clinometer. 

Christen's stick is not accurate enough for the measurement of trees 
over 100 feet high. It does not require the measurement of distances. Its 
form is improved by Pinchot. 

PARAGRAPH XXXIV. 

FACTORS INFLUENCING THE EXACTNESS OF HYPSOMETRICAL OBSERVATIONS. 

The best results are obtained if the distance between tree and observer 
equals the height to be measured. In sighting towards the spreading top 
of a hardwood tree, the observer is apt to overrate the height, the tip 
being buried in the spreading crown. The line of sight strikes the edge 
of the crown instead of striking the apex of the crown. 

Timber cruisers are usually satisfied to determine the number of logs 
obtainable from the bole instead of determining the length of the bole. 
As a matter of fact, where the tree furnishes saw logs only, the total 
height of the tree is a less reliable indicator of the total contents than 
the length of the merchantable bole. 

Instruments like Faustmann's, Kcenig's and Pressler's cannot be used 
in windy and rainy weather. Dense undergrowth and dense cover over- 
head render exact measurement impossible. 

PARAGRAPH XXXV. 

INDIRECT MENSURATION OF DIAMETERS. 

The following instruments are used to measure the diameter of the tree 
at any point of bole : 

a. Winkler, an addition to Kcenig's measuring board. 

b. Klausner. 

c. An ordinary transit. 

d. Wimmenauer's telescope. 

PARAGRAPH XXXVI. 

PRESSLER'S TELESCOPE. 

Pressler's telescope is used to find the "guidepoint" and the "rectified 
height," as defined in Paragraph XXVIII., 3. The diameter chest-high 
is taken between the nails at the end of the instrument. Then the tele- 
scope is pulled out to a length double the original, divided by the cosin 



24 Forest Mensuration 

of the angle found between the horizon and the probable sight to the 
"guidepoint" (at which the observer expects to find one-half the diameter 
chest-high). Thus, actually, the instrument merely examines the correct- 
ness of an original estimate. 

The Pressler telescope can be used for finding the merchantable length 
of any bole. Merely place a stick, equal in length to twice the minimum 
diameter permissible in a merchantable log, at the foot of the tree, catch 
it between the nail points and proceed as described. 

PARAGRAPH XXXVII. 

AUXILIARIES FOR CALCULATION. 

Auxiliaries for calculation are : 

1. Sectional area tables (Schlich, Vol. III.); engineering books like 
Haswell's; Bulletin 20; also Green.) 

2. Ideal cylinder tables (Schlich and Bulletin 20). 

3. Multiplication tables and logarithm-tables. 

4. Tables showing contents of logs in any of the 43 rules, according 
to length and diameter. 

PARAGRAPH XXXVIII. 

TREE VOLUME-TABLES. 

Tree volume tables have been constructed on a very large scale for the 
leading species in the old country. In the United States, the Government 
is now beginning to make such tables. The tables give the cubic, dumber 
and cord wood contents of trees, according to species, diameter and some- 
times according to total height and merchantable height (number of logs). 

Bulletin 36 reprints the following tree volume tables : 

A. According to diameter measure merely. 

Page 92. Adirondack White Pine, volume in standards. 

Page 94. Pennsylvania Hemlock, volume in feet, b. m., Scribner. 

Page 94. Adirondack Hemlock, in standards. 

Page 95. Adirondack Spruce in standards. 

Page 96. Adirondack Birch, Beech, Linden, Sugar Maple in Scribner, 
feet, b. m. 

Page 96. Adirondack Balsam, in standards. 

Page 97. Adirondack White Cedar, in standards. 

Page 98. Arkansas Shortleaf Pine, in feet, b. m., Doyle. 

Page 98. Missouri Ash, Elm, Maple, Cypress, Gum, Oak, Hickory, 
Poplar, in feet, b. m., Doyle. 

Page' 99. Western Yellow Pine, in feet, b. m., Doyle (Black Hills), dis- 
tinguishing between the volume of first and second growth. 

Page 99. Yellow Poplar in Pisgah Forest in feet, b. m., Doyle, distin- 
guishing between good, average and poor conditions of 
growth. 



Forest Mensuration 25 

All tables, except Yellow Poplar tables, are based on the measurement 
of a large number of trees. The Yellow Poplar tables are based on stem 
analyses of a small number of trees. 

B. According to measurement of height and diameter combined. 

Page 93. Wisconsin White Pine (height expressed by the number of 

logs obtainable from merchantable bole) in feet, b. m., Doyle. 
Page 103. Adirondack Spruce expressed in feet, b. m., Scribner, the 

total height of trees being measured. 
Page 104. The same in cubic feet. 
Page 105. The same in cords for pulp wood. 
Page 106. New Hampshire Spruce in feet, b. m., in New Hampshire 

cubic feet sanctioned by law. 
Pages 108 and ill. Adirondack White Pine with bark, expressed in 

cubic feet. 
Page no. Adirondack White Pine in feet, b. m., Doyle. 

Monographic investigation into the growth of the leading American spe- 
cies is of great importance. The trees of virgin forests are very defective, 
however, and tree tables can never be constructed giving the contents of 
defective trees. 



SECTION III.— VOLUME OF FORESTS. 
PARAGRAPH XXXIX. 

SYNOPSIS OF METHODS FOR ASCERTAINING THE VOLUME OF FORESTS. 

The methods used to find the volumes of entire forests, of forest com- 
partments, tracts, quarter sections, coves, etc., are : 

1. Estimating (Par. XL.). 

2. Exact calculation after measurements (Par. XLI., f. f. ). 

3. Combined measuring and estimating (Par. IL., f. f.). 

Obviously, measuring without estimation is possible only in forests con- 
taining little unsound timber. 

PARAGRAPH XL. 

ESTIMATION OF FOREST VOLUME. 

In primeval woods, where a few assortments only are salable and where 
stumpage is cheap, the estimation of stumpage necessarily takes the place 
of the measurement. If any measurements are taken, they are merely 
meant to back the estimation of the cruiser. The more defective the trees 
are, the more preferable is judgment and local long experience in the mill 
and in the woods on the side of the cruiser to mere measuring. 



26 Forest Mensuration 

The volume of a wood is ascertained by cruisers' estimates in the fol- 
lowing ways : 

a. By estimating the number of trees and the volume of the average 

tree with due allowance for defects. 

b. By counting the trees and estimating the volume of average trees 

with allowance for defects. 

c. By estimating the volume of each tree separately, sounding it with 

an axe, when necessary, and judging its soundness from all 
sides. 

The above methods (a, b, c) are applied either to sample plots or to 
sample strips or to the entire area. 

A blazing hammer is often used to prevent duplication; the revolving 
numbering hammer might be used in case of scattering trees, so as to 
allow of control of the estimates by the owner, his forester or the pros- 
pective purchaser of stumpage. 

In irregular forests — hardwood forests of the United States — the only 
safe way is separate estimating of each individual tree after careful in- 
specting. Incredible errors result from wholesale and rapid estimates. 

In the case of even aged woods, a look at the height growth and a 
knowledge of the age gives a good idea of the forest's volume. Under 
very poor conditions of growth, the annual timber production per acre 
and year is as little as 15 cubic feet; under the best conditions it is as 
much as 250 cubic feet per acre and year. On an average (on absolute 
forest soil), 50 cubic feet per acre and year may be considered as the 
production of healthy and densely stocked forests. 



PARAGRAPH XLI. 

PRINCIPLES UNDERLYING THE EXACT MENSURATION OF FOREST VOLUME. 

The basis of any exact measurement of volume is formed by a survey 
of the sectional area, combined with an account of the number of stems ; 
sectional area and number are found by calipering (valuation survey). 
Whatever rule of log measurement may be at stake, the total sectional 
area of the forest is always of first importance for a survey of forest 
volume. Next in importance is the calipering of sample trees, followed 
by an exact survey of their volume. The ratio r existing between the 
volume of the sample trees (expressed in any unit or mixture of units) 
and the sectional area of the sample trees is identical with the form 
height (compare Par. XXXII., towards end) of the sample trees. The 
form height of sample trees properly selected is the form height of the 
forest. The sample trees are usually cut and worked up into logs, cord- 
wood, tannin wood, etc., for the purpose of volume survey. 

V v f. h. s. 

— — _ = and V — S. f. h 

S s s 



Forest Mensuration 



27 



If the trees of the forest are defective, the sample trees should exhibit 
average defects. 



PARAGRAPH XLII. 

FIELD WORK FOR EXACT VALUATION SURVEYS. 

The valuation survey requires : 

1. Calipering of all trees; the diameter is taken in inches or in multi- 
ples of inches. Each species and each height class or age class are or 
may be taken separately. 

2. Entering the takings on tally sheets, arranged as follows : 



Diameter. 


Spruce. 


Beech. 


Height classes. 


Height classes. 




I 


II 


I 


II 


10" 










n" 










12" 










13" 
etc. 











The larger the trees are, the bigger is the permissible interval of 
calipering. If trees average two feet in diameter, an interval of 3 inches 
is permissible, provided that a large number of trees are calipered. 

It is a strange fact that the diameter measured from east to west is 
larger on the whole than the diameter from north to south. 



PARAGRAPH XLIII. 



BASAL ASSUMPTIONS. 



The only assumption made in calculating the volume of the forest after 
Paragraph XLI. is that the form height of the sample trees equals the 
form height of the forest. No other estimate or assumption is being 
made. This premise is much safer than the assumption that the volume 
of the forest bears the same ratio to the volume of the sample trees 
which the number of trees in the forest bears to the number of the sample 
trees. More unsafe is the assumption that the volumes of forest and 
sample trees bear the ratio of the acreage occupied by the forest on the 
one hand and by the sample trees on the other hand. 



28 



Forest Mensuration 



PARAGRAPH XLIV. 



SELECTION OF SAMPLE TREES. 



Sample trees are selected either irregularly or after a regular plan. In 
the latter case, it is best to distribute them equally among the diameter 
classes composing the forest (Draudt-Urich method and Robert Hartig 
method), instead of selecting sample trees of average diameter. 

It is more important that the sample trees should have proper average 
class-form height (and average defects) than that they should have exact 
average class-diameters. 

PARAGRAPH XLV. 

DRAUDT-URICH METHOD. 

The Draudt-Urich method is in common use abroad for measuring 
the forest. The trees of the forest are divided into a number of classes 
(usually five). Each class contains an equal number of trees, class I 
containing the largest and class 5 the smallest trees. In each class an 
equal number of sample trees, having about the average diameter of the 
class, are felled and worked up into logs, cordwood, ties, poles, etc. The 
form height of all sample trees is obtained as the quotient of their volume 
(in any unit or mixture of units) divided by their sectional area. Mul- 
tiplying the sectional area of the forest with this form height, the exact 
volume of the entire forest and its composition (logs, poles, cords, etc.) 
are given by one operation. 

Sample trees of the average diameter of a class are found by dividing 
the sectional area of the entire class by the number of trees per class. It 
is wrong to find the average diameter by dividing the sum total of the 
diameters by the number of trees. 



Diameter 
Breast High. 


Number 

of 
Trees. 


Diameter 
Classes 
of Trees. 


Number 

of Sample 

Trees. 


Average Diam- 
eter of Sample 
Trees. 


40" 
35" 
30" 

25" | 
20" 

15" j 

( 

10" \ 

1 


310 

240 

506 

1226 


I 


1 1 


29" 


9 
1040 

1233 


II 


1 1 


17" 


1847 
435 


III 


1 1 


14" 


2282 


IV 


1 1 


10" 


! 
1 


2282 


V 


1 1 


10" 



Forest Mensuration 29 

The advantages of the Draudt-Urich method are : 

r. All sample trees can be worked up in a bunch. 

2. Not only the entire volume but as well the different grades of tim- 
ber, fuel, ties, etc., composing the volume are found by one operation. 

A large number of sample trees are, however, required, and, since the 
volumes of the various classes are unequal, a negative mistake made in 
establishing the volume of one class is not apt to be counter-balanced by 
a positive mistake made in finding the volume of another class. 

PARAGRAPH XLVI. 

ROBERT HARTIG METHOD. 

Robert Hartig's method forms tree classes containing equal sectional 
areas— not equal numbers of trees. An equal number of sample trees is 
cut in each class and worked up separately for each class. The volume 
of the forest is also obtained separately for each class. Otherwise, the 
manner of proceeding is identical with that of Paragraph XLV. 

Preferable it would seem to cut in each class a number of sample trees 
having, in the aggregate, the same sectional area. This scheme, how- 
ever, would represent the big-diameter class by an absurdly small num- 
ber of samples. 

PARAGRAPH XLVII. 

AVERAGE SAMPLE TREE METHOD. 

If average trees of the entire rorest are taken as samples, then the 
volume of the forest is obtained with smaller accuracy. 

The proportion which the different assortments of timber, wood, bark, 
etc., form in the entire output is not clearly shown by such sampling. 

In a normal, even-aged wood the tree of average cubic volume is found 
by deducting 40% from the total sectional area, beginning with the de- 
duction at the biggest end. The largest tree then left is, or happens to 
be, the average tree of the wood. 

PARAGRAPH XLVIII. 

EXACT MENSURATION WITHOUT CUTTING SAMPLE TREES. 

Frequently the cutting of sample trees for the purpose of a valuation 
survey is not feasible. The volume of the forest in cubic feet — but not 
the assortments composing the volume — may then be ascertained as fol- 
lows : 

a. Take the total sectional area of the forest according to diameters 
and species and, if necessary, according to height classes. 

b. Ascertain the bole volume of some available trees with the help of 
Pressler's tube or by indirect measurement of heights and diameters. 



30 Forest Mensuration 

c. Proceed as indicated in the last three paragraphs, keeping in mind, 
however, that only the cubic volume of the boles is thus obtainable. The 
branch-wood-percentage or the timber-percentage of the bole must be 
estimated. 

The Hartig method (Paragraph XLVI.) might be combined with the 
use of Pressler's telescope, and the bole volume of a wood above breast 
height might be ascertained as 2/3 of the total sectional area of the 
forest, multiplied by the arithmetical mean of the rectified heights of 
the sample trees representing the various diameter classes. 

2 S (r t + r 2 + r-3 + r 4 + r„) 
V = X 

3 5 

The bole volume below breast height in cubic feet is equal to the 
sectional area of the wood times 4J/2. 

PARAGRAPH XLIX. 

COMBINED MEASURING AND ESTIMATING. 

If measuring and estimating are combined, the following typical meth- 
ods may be used to ascertain the volume of woods : 

1. The form factor method (Paragraph L.). 

2. The form height method (Paragraph LI.). 

3. The volume table method (Paragraph LIL). 

4. The yield table method (Paragraph LIIL). 

These methods might be used in connection with the so-called "dis- 
tance figure" of Paragraph LIV. 

In applying these methods, one or the other of the three factors of 
volume (sectional area, height and form factor) are obtained by estima- 
tion. 

The paragraphs following Paragraph LVIII. give a number of methods 
practically used and also based on combined measuring and estimating. 

PARAGRAPH L. 

FORM FACTOR METHOD. 

The form factor method ascertains the sectional area by calipering, 
according to species, and, if necessary, according to height classes. The 
average height of the wood (by species, classes) is obtained by actual 
hypsometric measurement. The form factor is read from local form 
factor tables. 

The average height is obtained — not as the arithmetic mean of a num- 
ber of heights measured, but much more — correctly from the ratio exist- 
ing between the sum total of the ideal cylinders and the sum total of 
the sectional areas of the trees hypsometrically measured. The form 
factors appearing in form factor tables must be averages obtained by 
many hundreds of local measurements. 



Forest Mensuration 31 

Mistakes amounting to up to 25% in the sum total of the volume 
obtained by the form factor method are not impossible, since average 
form factors appearing from a form factor table are often at variance 
with the actual form factor. 

Form factor tables for American "second growth" are still lacking. In 
primeval woods the form factor method seems out of place. 



PARAGRAPH LI. 

FORM HEIGHT METHOD. 

The form heights of merchantable trees are, generally speaking, sub- 
ject to only small variations. Those, e. g., for Adirondack White Pine 
scaling from 18" to 36" in diameter breast-high are (for standard rule) 
close to 1.25. 

Multiplying the sectional area of a White Pine woodlot (say 100 square 
feet) by the form height previously obtained through official measure- 
ments (like those by T. H. Sherrard), the volume of the woodlot — in 
the present example about 125 standards — is easily obtained. 

Form height tables based on feet b. m., Doyle, are not as simple as 
those based on the standard rules and cubic foot rules, owing to the 
mathematical inaccurary of Doyle's rule, which causes the form heights 
to be pre-eminently dependent on the diameters. 

Form height tables should be constructed for the leading merchantable 
species in the United States. Of course, such tables are more readily 
applicable to second growth than to first growth. 

The form height tables should exhibit the number of standards, cords, 
ties, etc., obtainable per square foot of sectional area in each diameter 
class. In case of defective trees, proper allowance must be made for 
defects — rather a hazardous risk in primeval hardwoods. 



PARAGRAPH LII. 

VOLUME TABLE METHOD. \^_l-3--<S <Fv WaX- /0^-^i_vj ' V 

In Paragraph XXXVIII. a number of volume tables have been enum- 
erated, from which the volume of trees of given species and diameter 
(and height) can be readily read. 

A valuation survey of the forest (or of a woodlot or of a sample plot) 
yields the diameters of the trees stocking thereon. The number of 
trees found for each diameter class is multiplied by the contents of a 
tree of that diameter appearing from the volume table. The sum total 
of the multiples is the sum total of the volume of the forest. 



32 



Forest Mensuration 
Sample. 



u 
+J 

B 


Yellow Pine. 


Hickory. 


Oak. 


03 

s 


No. 
trees. 


Average 
volume. 


Total 
volume. 


No. 
trees. 


Average 
volume. 


Total 
volume. 


No. 
trees. 


Average 
volume. 


Total 
volume. 


12 

15 

18 

21 

24 

27 

30 

33 
36 


30 
42 
17 
36 
33 
20 
10 
1 
1 


60 

I20 

300 

520 

780 

1080 

1420 

1800 

2200 


I .800 

5.040 

5.IOO 

18.720 

25.740 
2 I . 600 
14. 200 

1 . 800 

2 . 200 


7 

9 

18 

5 

12 

6 

3 


140 
240 
370 
500 
660 
840 
1050 


980 
2160 
6600 
2500 
7920 
5040 
3150 


14 
5 
23 
22 
22 

7 
10 

5 

5 


160 

200 

350 

520 

730 

940 

1 1 50 

1400 

1800 


I .400 

I .OOO 

8.050 

1 1 . 440 

i 6 . 060 

6.580 

1 1 . 500 

7 .000 

9.000 














Totals . 






96 . 200 






28.350 






72.030 



Grand total 196.580' B. M. 



The volumes of the column "Average Volume" are taken from tables 
published by the Bureau of Forestry. 



PARAGRAPH LIII. 



YIELD TABLE METHOD. r>sv 



^XXV. ^M^x 



^ 



All over Europe local yield tables are used to quickly ascertain the 
volume of pure, sound, even aged woods. For America, such yield tables 
— normal local yield tables — exist only in the white pine tables given in 
Pinchot and Graves' pamphlet, "The White Pine." 

The method of construction of yield tables appears, from Paragraph 
XCII. and following. 

Under yield tables are understood "acre-volume-tables," whilst under 
volume tables are understood "tree-yield-tables." 

Normal yield tables specify the age of even aged and pure woods, the 
height of such woods and the volume (by assortment) of such woods, 
according to the productiveness of the soil. An indication for the latter 
is found in the height growth. 

Such yield tables hold good only for woodlots normally stocked. A 
woodlot is normally stocked "when all local factors of wood production 
have pronounced themselves unhampered in the annual production of 
fibre." Normal woods, even of small extent, are extremely rare. In Ger- 
many the average wood lacks 25% of being normal. Since the normal 
yield tables give the yield for normal conditions only, a deduction must 
be made from the volume indicated by the yield table when applied to 
a given woodlot, according to the abnormality of the same. 

Proceed as follows : 



Forest Mensuration 33 

Ascertain age and average height of the trees ; find the yield table 
which gives a similar height for the same age; reduce the volume indi- 
cated by this yield table and for this age, by estimating the deficiency of 
the growing stock. 

Obviously, there is much room for guessing, since neither height nor 
form figure nor sectional area in woodlots abnormally stocked can lay 
claim to normality. 

Schuberg, denying a truism otherwise generally acknowledged, claims 
that the height alone does not indicate the productiveness of the soil. 

At present, normal yield tables are of little use in American forestry. 



PARAGRAPH LIV. 

DISTANCE FIGURE. 

Under "distance figure," an invention of Koenig's, is understood the 
quotient a formed by the side / of the average growing space of a tree 
(considered as a square) and by the diameter of the average stem d. 

1 
a = — 

d 

The average distance from tree to tree and the average diameter of a 
number of trees is obtained by a number of measurements in the forest. 
If the area of the forest is F square feet, then the sectional area of the 
forest is 

7T F 

= — X — square feet 
4 a 2 

The actual test proves the fallacy of Koenig's assumptions. The ex- 
planation lies in the fact that the average diameter of a wood is not the 
arithmetical mean of the diameters composing it. Further, the growing 
space of a tree is not a square. 

The actual growing space per tree can be correctly ascertained by laying 
a sample strip through the forest, counting at the same time the trees 
within the strip. The sectional area of the forest is obtainable, however, 
without greater trouble and with much greater accuracy, from the pro- 
duct calipered sectional area of trees in the sample strip times area of the 
forest over area of the sample strip. 

On an acre of average soil, there is on an average room for the fol- 
lowing numbers of healthy trees, according to age : 



At 20 years 1,600 specimens. 
At 50 years 600 specimens. 
At 100 years 240 specimens. 
At 150 years 150 specimens. 



34 



Forest Mensuration 



PARAGRAPH LV. 
algon's universal volume tables. 

So-called "universal volume tables" have been constructed by H. Algon, 
a Frenchman. For a description of these tables see "Indian Forester" 
of July, 1902. 

The volumes given for each diameter of trees, whatever the species be, 
are presented on a number of tables as follows : 





Volume in Cubic Feet. 


Diameter. 














Tabk 


: 1. Table 5. 


Table 10. 


Table 15. 


Table 20. 


6" 


2 


3- 


4- 


6. 


8. 


9" 


5 


8 




10 




16. 


18 




12" 


9 


15 




21 




27. 


33 




15" 


19 


28 




39 




50. 


61 




18" 


27 


39 




59 




69. 


84 




21" 


43 


60 




83 




109. 


128 




24" 


54 


78 




108 




138. 


168 




27" 


72 


107 




147 




188. 


228 




30" 


87 


129 




177 




228. 


276 




33" 


in 


163 




221 




288. 


349 




36" 


129 


189 




258 




333- 


405 





The tables are used as follows : 

1. Caliper the entire forest according to diameters and species. 

2. Measure a number of type trees, selected at random, after felling 
them. 

3. Find that volume table amongst the 20 tables given which best cor- 
responds with the diameters and volumes of the type trees. Apply the 
volume table, which is found to be the proper one, to all diameter classes 
calipered in the woods. 

Objections to the method are: 

a. The danger of mistakes is very great. In an absolutely even aged 
wood, one tree of 15 inches diameter may easily show 50% more volume 
than another tree of the same diameter, the latter being more tapering 
and shorter. 

b. In an uneven aged wood the tables are necessarily wrong because 
the form height is a function of age as well as of height and diameter. 

c. The method does not give any idea of the proportion of logs, fuel, 
bark, etc. 

Algon calls these tables "universal" assuming that they hold good for 
all species of the universe. 



Forest Mensuration 35 

PARAGRAPH LVI. 

schenck's graphic method. 

This method, as well, can be used only for sound woods. No calcu- 
lation is required. The procedure is : 

1. Caliper the whole wood. 

2. Cut sample or type trees of small, big and average diameters, find 
the contents of each tree separately, together with the composition of 
contents as logs, fuel and bark. 

3. On a piece of cross section paper, use as many units along a hori- 
zontal line as there are trees (or tens or hundreds of trees) calipered. 

4. Mark the unit which each sample tree, according to its diameter, 
would occupy if the biggest tree were placed to the right and the smallest 
to the left of the horizontal line. 

5. Enter over the marked units the volume of the type trees (accord- 
ing to the composing factors, if required) in square units. A square unit 
might correspond with ten feet board measure, or with 1/100 of a cord, 
etc. 

6. Draw a line joining the ends of the columns, adjusting it by an 
average curve. 

7. Measure the space (in square units) between the curve and the 
horizontal line with the help of a planimeter; the number of square units 
giving directly the number of feet Doyle, or of cords, etc. 

If there are several assortments of volumes, several curves must be 
drawn. This method allows of separating the volumes of trees allotted 
to the several diameter classes. Mathematical errors are, practically, 
excluded. 

PARAGRAPH LVII. 

FACTORS GOVERNING THE SELECTION OF A METHOD OF VALUATION SURVEY. 

In the case of a valuation survey ("stock taking") in the woods, the 
following points must be considered : 

a. The degree of exactness required, which depends on the purpose 
at stake {c. g., scientific investigations, or preparation for logging, or 
taxation). 

b. The regularity, uniformity and soundness of the growing stock. 

c. The minimum diameter of logs ; assortments ; marketability of spe- 
cies. 

d. The possibility of cutting sample trees. 

e. The expense permissible. 

The question usually arises whether the entire forest or sample plots 
only must be surveyed. The answer depends on the configuration of the 
ground, uniformity of the growing stock as to size, age, species and 
quality of its components ; further on the value of stumpage, on the accu- 
racy required, on the available time and on the available funds. 



36 Forest Mensuration 

The following METHODS OF VALUATION SURVEYS might be 
distinguished : 

I. Cutting sample trees. 

a. Sample trees selected for about five diameter classes, each 

class containing about one-fifth of the number of trees pres- 
ent (Draudt-Urich method). 

b. Sample trees selected for about five diameter classes, each 

class containing about one-fifth of the sectional area of all 
trees present (Robert Hartig method). 

c. Sample trees selected as average-diameter-trees of the entire 

forest (Old Bureau method). 

d. Sample trees selected at random — c. g., from dead and down 

trees (C. A. S. method — applied in the Balsams; Algon 
Universal tables; Graphic method). 

e. Stem analysis, together w T ith investigations as to thickness of 

bark. 

II. Without cutting sample trees. 

a. Measuring height and diameter and estimating form figure of 

sample trees. 

b. Measuring rectified heights and diameters. 

c. Measuring merely diameters and estimating form heights. 

d. Photographing sample trees, having a scale — say a sti^k 6 feet 

long — on the picture. 

III. With the help of volume tables. 
IV. With the help of yield tables. 

PARAGRAPH LVIII. 

FACTORS INFLUENCING THE SELECTION OF SAMPLE PLOTS. 

If sample plots are taken, there must be determined: 

a. The number, situation and distribution of the sample plots. 

b. The absolute and relative size of the sample plots. The Bureau of 
Forestry prescribes sample plots equalling from I to 4 l A% of the forest. 
The "Forest Reserve Manual" prescribes 5% or more. 

c. The form of the sample plots and the manner by which the size of 
the sample plot is ascertained. 

In Europe an ordinary workman calipers, on an average, 5,000 trees 
(in maximo 12,000 trees) per day. In Pisgah Forest 500 trees is a good 
day's work for one estimator and one helper. 



Forest Mensuration 37 

• PARAGRAPH LIX. 

SIR DIETRICH BRANDIS' METHOD. 

The Brandis method is indicated where the object at stake consists in 
a rapid survey of the stumpage on large tracts, like the vast Teak and 
Bamboo forests of upper Burmah. 

Traversing existing trails of known length on horseback, the estimator 
records the diameter of each tree within a given distance (say 200 yards) 
on either side of the trail. 

The widths of the strips traversed multiplied by the length of the trail 
yields the area of the sample plot. The number of the trees of the 
various diameters found on the sample strip appears from the records. 



PARAGRAPH LX. 

PIXCHOT-GRAVES METHOD ADOPTED ON DR. WEBB'S ESTATE. 

1. Sample acres, measuring 4 x 40 poles, are irregularly laid into 
swamps, hardwood slopes and spruce slopes. The sum total of the sam- 
ple acres is 3^% of the total acreage. 

2. The length of a sample acre is actually chained off, whilst the width 
is ascertained (two poles to the left and two poles to the right of the 
chain) by tape, by pacing and by estimating. 

3. The sites of the sample acres are not marked on maps. 

4. All trees on the sample acres are calipered ; a number of heights 
are taken on each sample acre; for each sample acre the average diam- 
eter, the average height and the number of trees are ascertained. 

5. From these averages is deduced, for all sample acres, the average 
diameter, the average height and the number of trees. All these data, 
of course, must be given for the various species separately. 

6. From volume tables previously constructed the volume of the trees 
having average height and average diameter is obtained and is multiplied 
by the average number of trees. 

7. This multiplication yields the volume of the average sample acre. 
Objections to this method of valuation survey are: 

a. The tree of average diameter has neither average volume nor 

average height. 

b. The average diameter should be obtained from the fraction "total 

sectional area over number of trees." It cannot be obtained 
correctly from the fraction "sum total of diameters over num- 
ber of trees." Similar objections hold good for average height. 

c. Guessing at the width of a strip, in dense growth, is rather risky. 



38 Forest Mensuration 

Remark : Bulletin 36, page 125, states that volumes are now computed 
by the Bureau either by averaging the volumes found for the sample 
acres, thus obtaining the volume of a model acre as 

n 

(wherein n equals the number of sample acres) ; or by summing up all 
trees of each diameter class, by dividing each sum by the number of sam- 
ple acres, and by thus finding for a model acre the average number of 
trees for each diameter class. In both cases the volumes for each diam- 
eter class are read from volume tables. 

Allowance for defects is made according to local experience, all trees 
being calipered as if they were sound. 



"* PARAGRAPH LXI. 

THE GRIDIRONING METHOD. 

i. Work with compass (if a topographical map is required, also with 
barometer or clinometer) and with several tapes or ropes. These ropes 
are meant to denote the sides of a strip; within the strip the sectional 
areas are taken with calipers or Biltmore sticks. 

2. The tapes move continuously with the caliper men, and there is 
no stopping. The compass man keeps ahead of the measuring crew. One 
of the outside "tapers" has the correct length desired for a section. His 
tape must be run straight. The inner tapes may make snake linos. The 
tally man uses a fresh tally sheet for each section. 

3. All strips lie parallel and are equidistant. The width of the strips 
depends on the density of growth, smallest diameter calipered, available 
help and accuracy required. 

4. The distance between two parallel strips depends upon accuracy re- 
quired, width of strip and variety of configurations. 

5. Each strip is divided into sections of equal length. The tally sheet 
gives for each section the diameters (with bark) of the trees in that sec- 
tion ; further, remarks on the run and altitudes of ridges and creeks 
traversed, on roads, settlements, existing surveyor's marks, forest fires, 
forest pasture, previous lumbering and regeneration. The number of 
seedlings in a section might be approximately given under the same head. 



Forest Mensuration 



39 



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ft 

CD 

a 

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Trail or road. g. m. b. N 
Called # 


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CP 

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Few, eome, many seedlings of 

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40 Forest Mensuration 

Advantages of the gridironing method are : 

a. A topographical map is obtained at a slight extra expense. The 
original survey is controlled and the area of the tract is re-ascertained. 

b. Cruisers are forced to traverse all sorts of country and are not 
allowed to skip swamps, cliffs, etc. 

c. The proportion of flats, ridges, slopes, swamps, farms, or farm 
soil, pastures, etc., is found at the same time. 

d. The strips may be used as permanent statistical sample plots, if 
they start from definite points (corners) and run in definite directions. 

e. The procession of the cruisers is uninterrupted by stops; hence no 
loss of time. 

For a picture of a convenient tally sheet holder see Graves' Handbook, 
page 123. 

The gridironing method has been adopted by the working plan division 
in a somewhat altered form as follows (Bulletin 36, page 120) : 

1. Strips are always one chain (66 feet) wide. A section invariably 
comprises one acre equaling 1 x 10 chains. 

2. The measuring tape is trailing in the center of a strip ; two caliper 
men (proceeding one at the left, the other at the right hand of the tape) 
caliper a belt one-half chain wide, estimating the width at either side 
of the central tape. 

3. The compass man or tally man with the front end of the tape 
attached to his belt goes ahead and stops at the end of every chain, 
allowing the calipers to catch up. 

4. Thus there are ten stops for every acre; after 10 chains the tally 
man enters general notes. 

5. Heights may be measured by a separate crew. 

A crew of four men calipers in merchantable timber 20 to 40 acres 
per day; in small and merchantable timber from 15 to 25 acres per day; 
in longleaf pine up to 65 acres per day. 

PARAGRAPH LXII. 

FOREST RESERVE METHODS. 

Roth's Forest Reserve Manual gives three methods of valuation sur- 
vey, No. 1 and No. 2 being sample-area-methods, and No. 3 an entire- 
area-method. 

I. Sample circles with a radius of 20 yards, the circle containing 
J4 acre ; the radius is estimated, or paced from a central stick. Two 
sub-methods are permitted, namely : 

a. Count the number of trees of merchantable size ; estimate the aver- 
age tree according to log length, taper and thickness of bark; estimate 
the percentage of defectiveness (from 10% to 40% after Manual, page 49). 



Forest Mensuration 41 

b. Caliper the trees in the circle into two-inch classes; estimate the 
average tree for each class and allow for defects as before. 

In both cases a map must show the site of the sample circles. The 
circle method is not allowed in scattering timber. At least 5% of the 
entire area must be sample-circled. 

2. Sample strips. Strips should be four rods wide, should run across 
ridges, should be shown on a map. Otherwise proceed as under 1. 

3. The "forty" method is used on surveyed land. It is an entire-area 
method applied to 40 acres. The sides of a "forty" are 80 x 80 rods, 
equal to 440 x 440 yards. Prescriptions : 

ij. Traverse each "forty" on lines about 100 yards apart, thus crossing 
4 times. 

b. Halt at every 100 yards and estimate the trees within a square of 
100 yards surrounding the stopping place. 

c. If possible, have a compass man control the length and the direc- 
tion of your runs. 

PARAGRAPH LXIII. 

SAMPLE SQUARES. 

Sample squares containing about one acre are used in Maine and in 
Northern New York. The side of a sample square is 14 rods. A cruiser, 
from the center of the square, under the density of the growth existing 
in Maine and New York, can overlook a circle of 7 poles radius sur- 
rounding him. Hence, as a matter of fact — or rather of theory — he skips 
the corners of the square, counting only the trees in a circle which has 
the side of the square for its diameter. The square contains 196 square 
rods, whereas the circle of 7 poles radius contains 155 square rods. The 
cruiser estimates the contents of all trees within the "square" from his 
central standpoint. 

PARAGRAPH LXIV. 

PISGAH FOREST METHOD OF 1896. 

i. The diameters of all trees promising to yield a log are measured 
in diameter classes of ^2 foot interval by a crew of 4 to 5 helpers armed 
with Biltmore sticks. 

The diameters are measured (or often estimated if beyond reach) at 
the point above which the tree is supposed to be sound. 

2. Each tree measured is marked by a blaze. The foreman enters on 
a tally sheet the species and the diameters called out by the helpers. A 
special tally sheet is used for each cove. 

3. The average contents of the diameter classes are estimated with the 
help of sample trees selected for each species and each diameter — a very 
uncertain estimate owing to the unsoundness of the trees. 



42 



Forest Mensuration 



4. Each cove is numbered or lettered to correspond with the tally 
sheet on a tree standing at the outlet of the cove. 



PARAGRAPH LXV. 

PISGAH FOREST METHOD FOR STUMPAGE SALE, BARK SALE AND LUMBERING 

OPERATIONS. 

i. Each tree is approached individually, its diameter measured and its 
defects, especially its hollowness, examined by "sounding." The diam- 
eter measure and the estimated volume are entered on a tally sheet oppo- 
site the number of the tree, which is inserted in the stump of the tree 
by a stroke of the "revolving numbering hammer." 

2. One cruiser and one helper tally 400 trees per day. 

3. The method allows of ready control by the owner, the forester and 
the buyer. It is adapted to hardwood forests in a rough mountainous 
country where the merchantable trees per acre are few; and where no 
tree is, practically, free from defects. (Compare Graves' Bulletin No. 
36, page 115). 

PARAGRAPH LXVI. 

HENRY GANNETT'S METHOD, ADOPTED FOR THE TWELFTH CENSUS. 

i. Base the estimate on the cruising reports obtainable from the local 
lumber companies and railroad companies. 

2. Control the applicability of the estimates to huge tracts by .travers- 
ing them and by overlooking them from a mountain top. 

Mr. Gannett expects that mistakes made in one county will be offset 
by those made in another. 

PARAGRAPH LXVII. 

A "FORTY" METHOD USED IN MICHIGAN. 

1. A "forty" (a square of 80 x 80 poles) is subdivided into 10 rectan- 
gles of 4 acres each, measuring 16 x 40 rods. 

2. The cruisers estimates when entering a rectangle. He counts the 
number of trees on every 4 acres and multiplies the number by the size 
of the average tree. 

3. For each "forty" the cruiser records in a memorandum the factors 
influencing the logging operations or the timber values, notably the 
swamps, ridges, forest fires, degree of defectiveness, facilities of trans- 
portation. 

A central line traversing the "forty" in a north and south direction is 
sometimes kept by a compassman assisting the cruiser. The outer lines 
of the "forty" are plain from the official survey marks. 



Forest Mensuration 43 

A number of variations of this method exist, according to the custom 
of local cruisers and according to the predilections of the lumbermen, 
largely governed by the value of stumpage. Compare Graves' Bulletin 36, 
page 116. 



PARAGRAPH LXVIII. 

DR. FERNOW'S "FORTY" METHOD USED AT AXTON. 

i. Each "forty" is subdivided into 16 squares of 2^2 acres each, the 
sides of a square being 20 x 20 poles. 

2. The head estimator, stepping from the corner of the square 10 
poles east (or west) and 10 poles north (or south) places himself in 
the center of the square. 

3. Helpers (students) are sent out, four in number, towards the north- 
east, northwest, southeast and southwest, each helper reporting the diam- 
eter and species of the trees found in that one-quarter of the 2^ acres 
which is allotted to him. 

4. The "forties" are carefully surveyed and surrounded by carefully 
trimmed lines. The outlines of the 2^2 acre sections are merely paced. 



CHAPTER II.— AGE 

PARAGRAPH LXIX. 

AGE OF TREES CUT DOWN. 

The age of trees cut down is found by counting the annual rings on 
a cross section (preferably an oblique cut) made as low above the ground 
as possible. Allowance must be made for the "stump years," by which 
is understood the number of years required by the top bud of the seed- 
ling, after sprouting, to reach the stump height ("cutting height," after 
Circular 445). 

Ring-counting in the case of even-porous hardwoods requires the use 
of a lens and of some coloring liquid (aniline and ferro-chloride) on a 
disc planed with a knife, a chisel or a hollow planer. 

The difference of the ring-numbers on the stump and the ring-num- 
bers at any place higher up indicates the number of years used by the 
top bud of the tree to traverse the intervening distance. Endogenous 
trees do not form any rings. 

False rings are formed under the influence of late frost, early frost, 
drought, fire and insect pests. They do not run all around the tree. 



44 Forest Mensuration 

As long as the tree lives, it must annually form a ring of growth (or 
rather an additional coat, the sleeves of which cover the branches), the 
outside of which becomes a layer of bark, the inside of which is a layer 
of wood. In tropical countries this rule does not hold good provided 
that there is no change of season. 

The formation of rings in the branches is regular. Branch-rings are, 
however, eccentric and elliptical. The formation of rings in the roots 
is said to be irregular, not representing the age of the root, possibly be- 
cause there is no or little change of seasons in the soil. 



PARAGRAPH LXX. 

AGE OF STANDING TREES. 

The age of standing trees can be estimated only when regular annual 
whorls of branches can be counted. 

The records of seed years and the history of the forest kept by many 
forest administrations usually give an idea of the age of the trees. 



PARAGRAPH LXXI. 

AGE OF A FOREST. 

The age of a forest is the average age of the trees composing it. 

In the case of a thicket suppressed for a long time by the superstructure 
of a leaf canopy overhead, a so-called "economic age" is frequently sub- 
stituted for the actual age. In the case of Adirondack spruce, for ex- 
ample, a diameter of I inch in the center of the trunk had better be 
counted, as, say, 15 years, although it may contain as many as 60 rings. 

The mean age of an uneven-aged wood is defined as follows : 

1. That number of years which an even-aged wood would require on 
the same soil, in order to produce the same volume as is now at hand. 

2. That number of years which an even-aged wood would require in 
order to produce at the time of maturity the same volume which the 
uneven-aged wood is likely to produce. 

The latter definition is scientifically more correct. Unless it is adopted, ' 
an uneven-aged wood may get over 20 years older in 20 years, owing 
to the fact that the trees dying in the meantime are mostly minors in age. 



Forest Mensuration 



45 



CHAPTER III.— INCREMENT 

SECTION I.— INCREMENT OF A TREE. 
PARAGRAPH LXXII. 

THE KINDS OF INCREMENT. 

The following kinds of increment must be distinguished : 

a. Increment of height, diameter, sectional area and volume. 

b. Current annual increment, current periodic increment and total in- 
crement. 

c. Average annual increment, average periodic increment and average 
increment at the age of maturity. 

d. Increment of the past and increment of the future. 

e. Absolute increment and relative increment. 

The increment of stems cut down is found by counting and measuring 
the annual rings on several cross sections. 

The term "stem" or "tree analysis" designates an investigation into the 
past height growth, diameter growth and volume growth of a tree. 

Circular 445 of the Bureau of Forestry defines the term "increment," 
somewhat narrowly, as follows : "The volume of wood produced by the 
growth in height and diameter of a tree or of a stand." 

For definition of the term "tree analysis," see Circular 445 of Bureau 
of Forestry. 

This circular distinguishes between : 

1. Stump-analysis, being a tree analysis which includes measure- 

ments of the diameter growth at given periods on the stump 
only, no matter what other measurements it may comprise ; 

2. Section-analysis, being a tree analysis which includes measure- 

ments of the diameter growth at given periods upon more 
than one section of a tree ; 

3. Partial tree (stump or section) analysis, wherein the measure- 

ment of the diameter growth at given periods covers a portion 
only of the total diameter growth. 



PARAGRAPH LXXIII. 

HEIGHT INCREMENT. 

The height increment, from the silvicultural standpoint, is of interest 
to the forester dealing with mixed woods. 

The difference between the number of rings found on two separate cross 
sections through the bole indicates the number of years which the tree 



4 6 



Forest Mensuration 



has required to grow through the distance lying between these two sec- 
tions. By counting the number of rings at several cross sections, one of 
which is made as close to the ground as possible, the current and the 
average height growth (increment) may be obtained by arithmetical or 
by graphical interpolation. 

A dense cover favors height increment. In rare instances, however, 
the stand of saplings or poles is so close that the height increment of 
the individual suffers from lack of food. 



PARAGRAPH LXXIV. 



THE CURRENT HEIGHT INCREMENT. 



In the high forest the current annual height increment reaches a 
maximum at an early age; passing this maximum, it sinks more or less 
rapidly. The culmination of the current annual height increment occurs 
the much earlier and its slackening after said culmination goes on at a 
more rapid rate if 

i. the species is fast growing and light demanding; 

2. the tree observed belongs to the dominant class ; 

3. the soil is good. 

For yellow pine the culmination of the current annual height incre- 
ment occurs amongst dominant saplings between the 10th and 15th years; 
for spruce at about the 20th year ; for beech and fir between the 25th 
and 30th years. Suppressed trees show the maximum of current height 
growth much later than dominant trees. 

As a general rule for all species, in case of dominant trees, the longest 
shoot is made 10 to 15 feet above ground. Slow growing species, shade 
bearers and trees stocking on poor soil reach that level at a later date 
than trees and species growing under reversed conditions. 

In the case of coppice forest, the maximum of the current height 
growth lies in the first three years of the life of the shoot. For oak 
coppice, the following table may serve as an illustration of height growth : 

Growth in Feet. 



Age in years 


10 


20 


30 


40 


5o 


Actual height 


13' 


23' 


30' 


37' 


43' 


Current annual increment 


1.3' 


1.0' 


0.7' 


0.65' 


0.63' 



PARAGRAPH LXXV. 

THE AVERAGE HEIGHT INCREMENT. 



The average annual height increment culminates later than the current 
annual height increment, and, after the culmination, it decreases at a less 



Forest JMcnsuration 47 

rapid rate than the current annual height increment. The average annual 
height increment culminates at the very age at which it is equal to the 
current annual height increment. 

As long as the average increment increases the current increment is 
larger than the average. The average increment still rises during a period 
of decrease of current increment. 

These laws hold good not only for height growth, but also for the 
growth of diameter, sectional area and volume. They are based merely 
on mathematical principles and are, for that reason, independent of spe- 
cies, climate and soil. 

If "a" denotes the current annual increment, and if "d" denotes the 
average annual increment, whilst the indices i, 2, 3, etc. (up to n), indi- 
cate the year of increment, then the following five equations hold good : 

n X d n = aj -(- a 2 -f a 3 + an 

(n 4. 1) d n + 1 = a t f a, + a 3 a u + a n +1 

(n + 1) d n + 1 = n X d n + an + 1 

n X dn + 1 = n X d u + a n + 1 — d n + 1 
n (d n + 1 — dn ) = an + 1 — d n + 1 



PARAGRAPH LXXVI. 

RELATIVE INCREMENT OF THE HEIGHT. 

The percentage of height increment forms, from the start on, an irreg- 
ularly descending progression. 

If the height is h at the beginning of a period of n years of observa- 
tion and H at the end of that period, then 

h X 1. op n equals H 

and 
n 

p equals 100.J— — 100 

Pressler substitutes for this formula in case of short periods of observa- 
tion the following : 

200 H — h 

n H +h 

This formula is derived as follows : Imagine that we are in the midst 
of the period of n years. At that time, the increment is apt to be 

— ^— , whilst the height at that time is apt to be — : hence, for that mid- 

n 2 

die year, the equation is : 

p H — h 2 

X 



100 n H +h 



48 Forest Mensuration 

PARAGRAPH LXXVII. 

DIAMETER INCREMENT. 

The current diameter increment is obtained by counting and measuring 
the rings on a disk through the tree. It is generally best to count from 
the bark towards the center, along two radii standing perpendicular to 
each other. 

The general laws of diameter growth are identical with those of height 
growth relative to culmination, decrease and increase of absolute (Par- 
agraph LXXV.) as well as of relative (Paragraph LXXVI.) increment. 

If we exclude the butt-piece below chest-height, the annual rings along 
the tree bole measured at various elevations above ground show a grad- 
ual increase of width with elevation, provided that the leaf canopy of 
the forest is complete and uninterrupted — e. g., the width of the ring 50 
feet from the ground, formed in 1903, is greater than the width of the 
ring formed 20 feet above ground in the same year. 

For trees standing in open crown-density, the width of the ring de- 
creases with the elevation above the ground, especially within the crown 
itself. 

A tree standing in a thin crown-density may show an even width of 
ring all over the tree bole. 

For very old trees in closed stand it is sometimes found that the diam- 
eter, say 40 feet above ground, is larger than the diameter, say, 20 feet 
above ground. 

The rings on a disk are not actually circles ; they more closely ap- 
proach the form of eccentric ellipses (see Paragraph XIII.). 

» 

PARAGRAPH LXXVIII. * 

SECTIONAL AREA INCREMENT. 

The increment of the sectional area is obtained from the increment of 
the diameters. Where greater exactness is required, and especially in 
case of irregular rings, the planimeter or the weight of a piece of paper 
having the form of the sectional area may be used for measuring to good 
advantage (Paragraph XIII.). 

The increment of the sectional area at chest height depends on the 
crown density overhead; further, on the quality of the soil. At chest 
height the culmination of the current annual sectional area increment 
takes place, in the case of dominant trees, fast growing species and com- 
plete cover overhead, between the years 40 and 70. 

The culmination of the current annual sectional area increment occurs 
always later than the culmination of the current height and diameter in- 
crement. After culmination it remains uniform for a long time. 

The absolute increment of a sectional area higher up on the bole, com- 
pared with the absolute increment at chest height, is found to be equal 
to it in the case of dominant trees ; larger in the case of suppressed trees ; 
and smaller in the case of isolated trees. 



Forest Mensuration 49 

Pressler establishes as the "law of bole formation" the following rule : 
"The absolute increment of the sectional area at any point of a bole is 
directly proportioned to the leaf surface above that point." 

This rule is, on the whole, correct. An unexpected swelling, however, 
is often found at 9/16 of the height of the tree. Within the crown of 
the tree, the decrease of sectional area increment is rapid. 



PARAGRAPH LXXIX. 

RELATIVE INCREMENT OF DIAMETER AND OF SECTIONAL AREA. 

The increment percentage at any point of the bole, like all increment 
percentages, forms a constantly but irregularly descending progression. 

At any point of the bole the increment percentage of the sectional area 
is the double of the increment percentage of the diameter. 

Schneider gives a handy formula for the sectional area increment per- 
centage, viz. : 

400 

P equals 

H nd 

wherein d represents the diameter at the beginning of the period of ob- 
servation, and wherein n indicates the number of rings per inch at the 
time of observation. 

The percentage of the sectional area increment increase along the bole 
with increasing height of the disk measured, excepting, however, possibly, 
the case of very isolated trees. 

The average sectional area increment percentage of the bole is found at 
a point a little below one-half of the total height, namely, at about 0.45 
of the total height from ground. 



PARAGRAPH LXXX. 

VOLUME INCREMENT. 

The (current and future) volume increment of standing trees is of 
great interest to forest financiers ; it can be estimated only, and cannot 
be measured exactly. 

The volume increment of trees cut down may be ascertained as follows : 

1. By the sectional method, or by "section analysis" (Paragraph 
LXXXL). 

2. From the increment of sectional area chest high, height increment 
and form figures (Paragraph LXXXIV.). 

3. From the increment of sectional area in the midst of bole (Para- 
graph LXXXV.). 

4. On the basis of the average annual increment (Paragraph 
LXXXVIL, last 4 lines). 

5 



V 



50 



Forest Mensuration 



PARAGRAPH LXXXI. 



SECTION ANALYSIS. 



The\section-method is a complete tree analysis by sections. The entire 
bole is divided into a number of sections, preferably of even length, at 
both ends, or, better, in the midst of which the periodical increment of 
the sectional area is ascertained (compare Paragraph XL). 

In the latter case, multiplying such sectional areas (in square feet) 
as belong to the same age of the tree by the length (in feet) of the sec- 
tions, the volumes (in cubic feet) of the different sections at given ages 
are obtained. 

The "top pieces," however, must be figured out separately, their length 
differing from the even length of the sections. These top pieces are 
usually considered as cones, and their volumes are ascertained as one-third 
height times basal area of top piece. The basal area of the top piece is 
identical with the upper area of the uppermost full section of a given age. 



Example for Huber-Sections Ten Feet Long. 



Total height 


25 feet. 


40 feet. 


67 feet. 




Total age 


20 years. 


40 years. 


60 years. 




Sectional area of Section i 


0.34 sq. ft. 


0.78 sq. ft. 


1.23 sq. ft. 


Sectional area of Section 2 


0.15 sq. ft. 


0.45 sq. ft. 


0.87 sq. ft. 


Sectional area of Section 3 




0.25 sq. ft. 


0. 64 sq. ft. 






Sectional area of Section 4 




0.03 sq. ft. 


0.53 sq. ft. 






Sectional area of Section 5 






0.25 sq. ft. 








Sectional area of Section 6 






0.04 sq. ft. 








Summary of sectional areas 


0.49 sq. ft. 


1.5 1 sq. ft. 


3.56 sq. ft. 


Summary sectional areas x 10 


4.90 cu. ft. 


15.10 cu. ft. 


35.60 cu. ft. 


Volume of top piece 


0.05 cu. ft. 


0.09 cu. ft. 


08 cu ft 






Total volume 


4.95 cu. ft. 


15.19 cu. ft. 


35.68 cu. ft. 





The volume of the top pieces forms in the older age columns an insig- 
nificant part of the total volume. 

If the logs as cut in the woods are used as sections, then each section 
has a separate length and its volume must be separately ascertained for 
every decade of age of tree. 

Remark : It is wise to first ascertain the full age of the tree, allowing 
for stump years. It is further wise to throw off that number of years 
which exceeds full decades — e. g., in case of a tree 117 years old, 7 years. 



Forest Mensuration 51 

At the stump the rings had best be counted from the inside out, allowing 
for stump years. Instance: Age of tree, 117; stump years, 4 years; count- 
ing on the stump, from the inside, 6 rings establishes the ring formed in 
the year 10. Continuing, the rings of the years 20, 30, 40, 50, etc., up 
to year no, are pencil marked. The outside seven rings are thrown off. 

At all other disk-sections, count and measure from the outside in, after 
discarding the 7 years exceeding full decades of tree life. 

PARAGRAPH LXXXII. 

noerdlinger's paper weight method. 

The total length of the tree is divided into 8 Huber sections, and cuts 
are made in the midst of these sections, at the height of 1/16, 3/16, 5/16, 
7/16 and up to 15/16 of the bole. On each cross section the radii are 
measured, not with the rule, but with dividers. 

On a piece of paper folded 4 times and thus divided into 8 sectors the 
measurements are entered with the help of the dividers, one sector being 
allotted to the first cross section, the next sector to the next cross sec- 
tion, etc. Multiplying the total weight of the zone indicating, say, the 
year 70, by height of the tree and dividing the product by the weight of 
a square foot of paper, the volume of the tree when 70 years old is 
directly obtained in cubic feet. Similarly the zones corresponding with 
the year 50, 60, etc., are cut out, weighed and multiplied. 

If the volume increment percentage p alone is to be obtained, then it 
is enough to divide, say, the "weight" of the year 70 by the weight of 
the year 60, and the 10th root of the quotient will equal i.op. 

PARAGRAPH LXXXIII. 
schenck's graphic tree analysis. 
Graphic tree analysis offers the following advantages : 

1. Mistakes are impossible, being at once noticeable on the diagram 
paper. 

2. The volume in feet Doyle can be readily obtained for any stated 
minimum diameter. 

3. The graphical sketch is adaptable to any of the 43 scales in use in 
the United States, as well as to the metric system. 

4. The thickness of heart wood and sap wood and bark readily appears. 

5. It is immaterial whether measurements are taken in meters or in 
feet, the graphical sketch readily allowing of transfers into other units. 

6. Height growth and diameter growth appear at the same time, and 
from the same entries. 

7. The length of the sections taken need not be uniform. 

The method of proceeding is as follows : On millimeter paper a system 
of co-ordinates is established; heights are entered as ordinates, diameters 



52 



Forest Mensuration 



or radii as abscissas. The scale for the height entries should be much 
smaller than that of the diameter entries. 

Diameter points, at the different section-heights, corresponding to a 
given decade of years are joined (beginning at the outside), by which 
procedure the outline of the tree at that decade is established. 

Th top cones are obtained by prolonging such outlines arbitrarily until 
they intersect with the height-axis. 

The merchantable bole for each decade is dissected, on the diagram, 
into logs the length and diameter of which are measured on the diagram. 



PARAGRAPH LXXXIV. 

wagener's method and stump analysis. 

Wagener recommends a partial stem analysis for cases in which a 
knowledge of the absolute increment, not a knowledge of the absolute 
tree volume, is required. Tree volume is sectional area chest high times 
height of tree times form factor. 

Wagener analyses : 

a. the height growth by counting the rings at various altitudes along 
the bole ; 

b. the growth of the sectional area at chest height by measurement in 
decades in the usual way. 

Wagener then estimates the form factor according to form factor tables. 

In the latter proposition, obviously, lies the danger of mistakes. Since, 
however, increment is a difference of volumes, merely the difference of 
mistakes — a comparatively small item — enters into the problem. ► 



Age in years 


60 


80 


100 


120 




14- 


17- 


19- 


21 . 






Sectional area b. h 


0. 25 


0.35 


0.50 


0.71 






Height in feet 


75- 


85- 


93- 


105. 






Form factor 


0.50 


0.50 


0.50 


050 






Volume in cubic feet 


9-4 


13- 


23- 


36. 








3- 


5 ic 


). 1 


3- 





The "stump analysis" (compare Paragraph LXXII.) introduced by 
the Bureau of Forestry rests on premises similar to those proffered by 
Wagener. 

If the form height for the stump-diameters (or the number of feet 
b. m. per square foot of stump area for given stump diameters) is known, 
the rate of volume increment can be quickly ascertained by mere stump 
analysis. 



Forest Mensuration 53 

It is, however, a well known fact that the diameter growth at the 
stump — especially at a low stump — is particularly unreliable as an index 
of volume growth, owing to the exaggerating influence on stump growth 
exercised by light, by water, by depth of soil and by superficial roots. 

Stump analysis as a means to bring a volume in reference to a sec- 
tional area at the stump is permissible only as a necessary evil. 

PARAGRAPH LXXXV. 

pressler's method. 

Frequently the task before the forester is merely that of ascertaining 
the increase of bole volume during the last 10 or 20 years. Then after 
Pressler, one single investigation into the growth of the sectional area is 
sufficient when made with the help of the accretion borer in the midst of 
the "decapitated" bole. The volume increment in cubic feet equals the 
sectional area increment in question multiplied by the height of the 
tree. 

The bole is decapitated by that number of top shoots which have been 
formed during the period of observation. This operation corresponds 
very well with the usual practice of judging the bole increment per- 
centage from the sectional area increment ascertained at 0.45 of height 
of tree. 

Pressler measures the sectional area at the end of the period of observa- 
tion too large, measuring it at too low a point. He multiplies this sec- 
tional area, however, by too small a height — namely, the decapitated 
height; thus a mistake made in the positive sense is apt to be eliminated 
by a mistake made in the negative sense. 

The axe can be used to better advantage frequently than the accretion 
borer. 

PARAGRAPH LXXXVI. 
breymann's method. 
Breymann gives the following formula : ' Kic^ 

1. For the current annual volume increment T: ^ "^.^, 



T = V ( 3 d + T) <~*^^^^~i ) 



wherein "8" and "A," denote the annual increase of diameter "d" and 
length ''1" respectively. 

2. For the corresponding increment percentage P: 

8 X 



P = 100(2- +T ) 



It appears that for trees of old age and hence of little height growth 
the increment percentage is merely dependent on the diameter increase. 



54 



Forest Mensuration 



Breymann, however, neglects : 

1. The change of form figure, during the period of observation; 

2. A number of small factors which ought to be embraced in the 
formula. 

For stopping height growth or for A, = , the term given for P can 
be easily reduced to the term given by Schneider for the sectional area 
increment percentage. 



' 



■ ~ -^ PARAGRAPH LXXXVII. 

FACTORS INFLUENCING THE CUBIC VOLUME INCREMENT. 



*M* 



■ 



A. 



The culmination of the current annual volume increment takes place at 
a later year than the culmination of the sectional area increment at breast 
■ • height. Naturally so, because with increasing age of a tree, its root sys- 
tem as well as the branch system, the feeders of the body, show contin- 
uous increase. 

Big and long branches, of course, require a great deal of wood fibre 
to increase and maintain their own strength, like levers increased in 
length. Hence, from a certain size of branch on, all wood fibre produced 
by the branch is used up within the branch itself, for its own purposes, 
instead of being added as increment to the merchantable bole. 

After Dr. Metzger, the crown of a tree yields the maximum of bole 
increment if its crown diameter is, and if the number of trees per acr<* 
are: 



Quality of soil. 


Diameter of crown, in feet. 


No. of trees per acre. 


Very good. 


16.5 


203 


Good 


14-7 


256 


Medium 


12.7 


343 


Poor 


9-3 


640 


Very poor 


8.3 


807 



From the theoretical standpoint it seems wise, consequently, to force 
the lower branches of a tree to die, with the help of proper tension and 
friction within the leaf canopy, when they exceed a length of 8.25, 7.35, 
6.35, 4.65 and 4.15 feet respectively (the halves of the diameters). 

Metzger's investigations are interesting, but his conclusions seem to be 
too sweeping. 

P. P. Pelton recommends the lopping of branches in order to shorten 
the length of the branch-levers. 

The average annual volume increment of dominant and sound trees 



Forest Mensuration 



55 



culminates at a very high age only, if ever, owing to the late culmina- 
tion of the current annual average increment. 

The volume increment percentage forms — as in all cases of increment — 
a steadily but irregularly decreasing progression. This percentage is in- 
variably equal to or higher than the sectional area increment percentage 
at chest height. 

Roughly speaking, the volume increment percentage amounts to from 
i to 1.7s times the sectional area (at chest height) increment percentage, 
or, as Pressler gives it, to from 2 to 3^2 times the diameter (at chest 
height) increment percentage. 



Crown;'covers part of bole 



■>. 



£ or more. 

itot 

Less than \. 



Wo 



>X * Height Growth. 



Seemingly nil. 



2.67 



Medium. 



2 . 67 - < •> 



Good 



v G °* 



.3.00 .« 
1-33UC 



Excellent. 



W t>ti ■■> ■> ■- < * - > 



3-i7U*^ 
3-33-1,1* V* 






#\ 



■V- 



Since the average volume increment of a tree is equal or closely equal 
to the current annual increment at a high age only, it is usually not 
permissible to substitute the average increment, which is easily ascer- 
tained, for the current annual increment. 



PARAGRAPH LXXXVIII. 

VOLUME-INCREMENT PERCENTAGE OF STANDING TREES. 

In the case of standing trees the volume increment percentage cannot 
be measured, owing to the impossibility of ascertaining a change of form 
height. 

The Pressler data given in the preceding paragraph allow of estimating 
the volume increment percentage of standing trees on the basis of a 
diameter-increase, measured at breast height. 

The Pressler "accretion borer" is used for the purpose, or an axe. 

Stoetzer, Director of the Forest Academy at Eisenach, modifies the 
Schneider formula for sectional area percentage, writing it 

C 
P = n¥ 

wherein n indicates number of years (rings) required to form one inch; 
d represents the diameter at the beginning of the period of investigation, 
whilst C (the so-called "constant factor of increment," which is not a 
constant factor at all) must be ascertained for a given species, soil, diam- 
eter, age and position by actual tests on felled trees. 

In old dense beech woods C is, e. g., 540. After a seed cutting in the 
same woods during the final stage of regeneration C is only 450 (observa- 
tion by Dr. Wimmenauer). 



56 Forest Mensuration 

Trees growing as cones would grow, have C equal to 600; trees grow- 
ing as Apollonian paraboloids would grow, have C equal to 800; after 
Stoetzer, C might amount to as much as 930, in case of suppressed trees. 
The minimum possible (in sound trees) for C is 400. 

The Pressler values given in the table of the preceding paragraph 
closely correspond with the constant factors of increment ascertained 
after Stoetzer. In the case of the Pressler table (at end of Paragraph 
LXXXVII.) we find, for medium height growth and very small crown, 
a factor 3.00 by which the diameter increment percentage is to be multi- 
plied. This factor 3.00 corresponds with 600 for a constant factor of in- 
crement. 

If the diameter in the midst of the bole is l / 2 of the diameter at the 
end, then the tree, it seems, is conical, and an increment factor of 600 
might be assumed. If the sectional area in the midst of the bole equals 
y 2 the sectional area at the end, then the tree is a paraboloid, and the 
increment factor seems apt to be 800. 

It must be remembered, however, that a tree forming a paraboloid 
grows as a paraboloid only, if its percentage of height growth is equal to 
its percentage of growth of sectional area — a rare case in merchantable 
trees. 

Similarly, a tree growing as a cone must have the height increment 
percentage equal to its diameter increment percentage. 

If n and v represent the number of rings per inch added to original 
diameters d and 8 at chest height and at 0.45 of the height of the tree 
respectively, then the "constant factor of increment C" is found as follows : 

400 C 

p (volume) 



v8 nd 
nd 



C = 400- 



PARAGRAPH LXXXIX. 

INTERDEPENDENCE BETWEEN CUBIC INCREMENT AND INCREMENT 
IN FEET B. M. DOYLE. 

Doyle's rule under-estimates the contents of small logs and over-esti- 
mates those of big logs. 

Consequently, the growth of a tree bole in feet b. m. Doyle is (for 
small trees yielding logs under 28" diameter) relatively faster than the 
growth of a tree bole expressed in cubic feet. The figures of Column D 
denote, in the following table, this excess rate of growth : 



Forest Mensuration 



57 



A 


5 


C 


D 




No. of ft. b. m. per 


Differences of con- 


"Extraordinary" 


Diameter of logs 


one eu. ft. of tim- 


secutive figures in 


percentage of incre- 


without bark. 


ber estimated 


Column B. 


ment Doyle co-in- 




after Doyle. 




ciding with 
1" growth. 


12" 


509 


0.41 


S.i 


13" 


5 SO 


o.35 


6.4 


14" 


5-35 


0-33 


5-7 


15" 


6.18 


0.26 


4.2 


16" 


6.44 


0.27 


4-3 


17" 


6.71 


0.22 


3-3 


18" 


6-93 


0. 14 


2. 1 


19" 


7.07 


0.26 


3-2 


20" 


7-33 


0.18 


2-5 


21" 


7-51 


0. 16 


2.2 


22" 


7.67 


0.15 


2.0 


23" 


7.82 


0.13 


i-7 


24" 


7-95 


0. 14 


1.8 


25" 


8.09 


0. 11 


i-4 


26" 


S.20 


0.12 


1-5 


27" 


8-33 


0.09 


1 . 1 


28" 


8.41 


0. 11 


1 . 1 


29" 


8.52 


0.08 


1 .0 


30" 


8.60 




... 



For the standard rules, the increment percentage of a tree can be ascer- 
tained by cubic measure as well as by standard measure. 

If n years are required to form one additional inch of diameter, then 
the extraordinary percentage of Doyle-increments amounts annually to 



yl.OD, wherein D represents the values of Column D in the foregoing 
table. 



By this factor -j/l.OD, the cubic volume increment percentage of a 
bole may be converted, ceteris paribus, into Doyle increment percentage, 
provided that 



58 Forest Mensuration 

i. The cubic increment percentage of the total bole coincides with the 
cubic increment percentage of the merchantable bole ; 

2. The merchantable bole does not increase in length during the period 
of observation. 

PARAGRAPH XC. 

CONSTRUCTION OF VOLUME TABLES. 

Volume tables are "tree yield tables" from which the volume of a tree 
of given species, given age, given diameter breast high or stump high, 
given height, given merchantable bole, given position (suppressed, dom- 
inant, etc., or isolated, crowded, etc.), given locality and so on can be 
readily read. The units of volume are cubic feet, board feet, standards, 
cords, etc., according to the requirements of the case. 

Obviously, volume tables give, or should give, the volumes of average 
trees ; they may give, in addition, the maximum and minimum volume 
possible in a tree of stated description. 

Volume tables are constructed either on the basis of hundreds (thou- 
sands) of measurements taken from trees actually felled in the woods 
(possibly also sawn at a saw mill, to ascertain the grades) or on the 
basis of a smaller number of complete section analyses. 

The rapidity of volume growth of a species and the development of its 
form height depend on many local factors — notably on climate, soil, sylvi- 
cultural systems at hand, influence of fires, fungi, insects, etc. 

Owing to the multitude of local factors influencing the volumes and 
the changes of volumes, local volume tables alone are entitled to & place 
in exact mensuration. 

Volume tables for second growth are more reliable than volume tables 
for first growth. 

Circular 445 of Bureau of Forestry defines volume table as "a tabular 
statement of the volume of trees in board feet or other units upon the 
basis of their diameter breast high, their diameter breast high and height, 
their age, or their age and height." 

The method of construction of volume tables is either mathematical or 
graphical. 

1. Mathematical method. 

The volumes ascertained for trees of a given diameter (breast high or 
stump high with or without bark), a given merchantable length or total 
length, a given age or a given quality or locality are added up. 

The sum total of these volumes divided by the number of trees forming 
it yields the average volume of the tree of stated description. 

These averages are shown, for the various diameters, lengths, ages and 
localities, in tabular form. 

The volumes corresponding with such diameters, lengths, ages and lo- 
calities, for which sample trees were not cut and measured, are found by 
arithmetic interpolation. 



Forest Mensuration 59 

Finally, the differences in volume shown by average trees of similar 
description (1. e., differing but slightly in diameter, length, etc.) are 
formed and rounded off in a manner causing the volumes to show a more 
steady mathematic progression. 

2. Graphic method. 

The volume of each tree measured is entered as the abscissa on a 
diagram-system of co-ordinates, whilst the diameters of the trees (or the 
age, etc.) are registered on the ordinate axis. Similarity of length is in- 
dicated by color of mark representing the tree; similarity of locality is 
indicated by the form of the mark (square, triangle, cross, circle, etc.). 

Corresponding marks are then joined by chains (having square, cir- 
cular, triangular links) of the proper color. 

Finally, average curves as well as maximum and minimum curves 
are drawn for the various colors and forms of marks. 

Maximum and minimum curves should not represent the very best 
and the very worst possibilities ; they should represent the average of 
very good and very bad trees. 

The graphic method is more reliable, because less depending on mere 
figures, than the mathematical method. Both methods are frequently 
combined. 

A number of complete tree analyses furnishes more reliable results than 
a large number of mere volume measurements because it yields more 
reliable curves (guide-curves) of development for one and the same lo- 
cality, and because it prevents the forester from drawing curves of growth 
at random. 

If the sample trees (or sample logs) are sawn up at a saw mill where 
the lumber is properly graded according to the inspection rules prevailing 
for the species in question, the volume tables may also give the actual 
average output of specified trees in lumber of the various grades. 



SECTION II.— INCREMENT OF A WOOD. 
PARAGRAPH XCI. 

INCREMENT OF FORESTS. 

The volume increment of the virgin forest is on the whole nill. 

In America the value increment of a primeval forest is based more on 
a price increment of stumpage than on a volume increment of trees. The 
volume increment, in addition, can scarcely be ascertained with sufficient 
accuracy for a given piece of forest at a reasonable expense. 

In second growth forests, on the other hand, say in Virginia, an abso- 
lute knowledge of the productiveness of the forest renders forestal invest- 
ments safer in the eyes of the owner ; and the safety of the investment it is 
which alone can tempt the capitalist to invest in forestry. A knowledge of 



60 Forest Mensuration 

the increment in second growth woodlands can be obtained from tabulated 
statements ("yield tables") showing the rate of growth for woodlands of 
a given species in a given locality. Under normal yield tables are under- 
stood such tables which give the rate of growth for even-eged, pure, nor- 
mally stocked, well thinned woodlots for given localities (compare Para- 
graph LIII. and XCIV..). 

Such normal yield tables are constructed abroad for beech, pine, spruce, 
fir and oak. In this country they exist only in Pinchot's and Graves' 
yield tables for white pine. In America, pure even-aged woods are found 
in rare cases only (taeda, echinata, rigida, jack and longleaf pines, tama- 
rack, coppicewood). 

In the construction of normal yield tables the following points require 
consideration : 

i. The different methods of construction (Paragraph XCIL). 

2. The combination, interpolation, adjustment and correction of the 
results (Paragraph XCIIL). 

3. The contents and use of yield tables (Paragraph XCIV.). 



PARAGRAPH XCIL 

METHODS OF CONSTRUCTION OF NORMAL YIELD TABLES. 

Normal yield tables may be based on : 

A. Repeated survey of some typical woodlots during their entire life- 
time. » 

B. Repeated survey of different woods standing on an equal quality 
of soil, during a period of years equal at least to the longest difference in 
age found amongst them. 

C. One-time, simultaneous survey of a very large number of woods of 
different ages standing on different qualities of soil. Missing links are 
here obtained by graphic or mathematical interpolation (Paragraph 
XCIIL). 

If tables are constructed by repeated survey of several woods (B), it 
is often found that the links cross one another for unexplainable reasons. 

PARAGRAPH XCIIL 

GATHERING DATA FOR NORMAL YIELD TABLES. 

In order to see whether or not two woods, in the case C of the pre- 
ceding paragraph, belong to the same chain of growth, two methods are 
in use : 

a. The horn or curve method, after Baur. 

b. The stem analysis method. 



Forest Mensuration 61 



Remarks on a: 



The contents and age of all woods (normal) surveyed are plotted in a 
diagram, the age forming the abscissa and the volume the ordinate of the 
system. 

Curves are then drawn outlining the maxima and minima of growth 
observed. 

The horn-shaped space between these curves is divided into a number 
of sectors equal to the number of yield classes to be distinguished. The 
middle line of each sector illustrates the productiveness of its class. 

The average height growth is obtained in a similar way, the height data 
forming the ordinates in a system of co-ordinates. 

Baur finds that the allotment of a given plot to a volume-sector corre- 
sponds with its allotment to a height sector. In other words, the height 
is, after Baur, an absolutely reliable indicator of the quality of the soil, 
or, what is the same, of the yield class. 

The growth of sectional area, height and volume being known, the 
development of the form factors for the various sectors is readily ob- 
tained from the fraction 

sXh 

Remarks on b: 

An analysis of the average stems in lots surveyed would not throw 
any light on their connection as members of one and the same chain 
of observation. After Robert Hartig, the 200 strongest trees are analyzed. 
After Wagener, the ideal cylinders merely of these 200 strongest stems 
are analyzed by ascertaining their height growth and their diameter 
growth at breast height. Weise and Schwappach are satisfied with an 
analysis of the heights merely of the 200 best stems. 

The selection of sample plots is not easy, even in second growth raised 
under forestal care. A valuation survey establishes for each plot the 
number of stems and the sectional area for each diameter class of stems 
(usually divided into 5 classes) ; further, the average age and the average 
height of the plot. The volume is then figured out, usually, according 
to the Draudt-Urich method. 

The experiment stations maintained by the European Governments 
control the growth of a large number of experimental plots, which should 
not be smaller than y 2 acre each. 

The sample plots are corner marked, and, more recently, the individual 
trees contained therein are numbered consecutively. Surveys of these 
plots are made every five years. The point of measurement is indicated by 
a chalk line. 

In America normal sample plots have not been established as yet by 
the Bureau of Forestry in second growth. The sample plots at Biltmore 
do not represent a normal second growth. 



62 Forest Mensuration 

PARAGRAPH XCIV. 

NORMAL YIELD TABLES, THEIR PURPOSES AND CONTENTS ABROAD. 

Normal yield tables are especially used for the following purposes: 

i. To ascertain the quality of the soil (c. g., for taxation). 

2. To ascertain the volume of the growing stock. 

3. To ascertain future yields of the forest. 

4. To solve problems of forest finance, especially those of forest ma- 
turity (length of rotation). 

German normal yield tables have the following contents : 

A. Tables for the main forest — the secondary forest comprising such 

trees on the same lot as are about to be removed by way of thin- 
ning : 

(1) Age, graded at five year intervals. 

(2) Number of trees. 

(3) Sectional area at chest height, inclusive of bark. 

(4) Average diameter. 

(5) Average height and height increment. 

(6) Volume in cubic measure arranged according to assortments 

as logs, fuel, bark, etc. 

(7) Periodical and average annual volume increment. 

(8) Increment percentage. 

(9) Form factor. 

(10) Normal growing stock. 

B. Tables for the secondary forest, giving merely its vol ume,» which, 
as stated, is to be removed by way of thinning. 

Circular 445 of the Bureau of Forestry defines "future yield tables" as 
follows : "A tabular statement of the amount of wood which, after a 
given period, will be contained in given trees upon a given area expressed 
in board feet or some other unit." 



PARAGRAPH XCV. **«■*« STVm »r \» * «* 

RETROSPECTIVE YIELD TABLES. 

In "retrospective" yield tables an attempt is made to rebuild the grow- 
ing stock as it was before lumbering from the stumps found on the 
ground and from stem analyses of the trees now standing. Prerequisite 
is a knowledge of the year in which lumbering took place and of the 
conditions of growth since prevailing. 

Method of proceeding: 

1. Make stem analyses and construct tree volume tables, showing the 
probable contents of trees for stumps of a given diameter and for given 
diameters b. h. 



Forest Mensuration 63 

2. On land cut over n years ago, find by valuation survey and stem 
analyses : 

a. The present volume "F." 

b. The volume "y" of the trees now standing as it was "n" years ago 
with the help of tree volume tables. 

c. From the stumps the volume "x" of the trees logged "n" years ago. 

3. A product of "F" units (with an undergrowth not fit for logging) 
has been derived in "n" years from an original stand aggregating "y" 
plus "x" units of volume. 

4. Grouping hundreds of sample plots together, yield tables for local 
use are obtained. Misleading is, of course, the multiplicity of conditions 
(mixture of species, soils, original stands, pasture and fire) surrounding 
a second growth which check the applicability and the combination of 
the tables found. 

The tables are way signs, not ways, toward a true knowledge of the 
productiveness of cut-over woodlands. 



PARAGRAPH XCVI. 

YIELD TABLES OF THE BUREAU OF FORESTRY. 

Bureau yield tables are meant to show the growth on cut-over land 
occurring within the next 10, 20 or 30 years, if a tract is logged to a 
10", 12" or 14" (or any other) limit. Bureau yield tables are based on 
tree volume tables and on an account of the numbers of tree individuals 
found in the various age classes of forest, viz., diameter classes of trees. 

The influence of the different qualities of soil on tree growth is not 
given, only one average volume table being constructed. The volume 
tables show the number of years which a tree requires to increase its 
diameter b. h. by one inch. The volume tables record, in addition, the 
volume increase corresponding with such diameter increase. Applying 
these findings to the stumpage presumably left after logging, the volume 
can be ascertained which is expected to be on hand 10, 20 or 30 years 
later. The volume growth is forecasted, as if it were taking place under 
primeval conditions. 

The Bureau neglects entirely the death rate of trees, due to natural 
causes and especially high amongst seedlings and saplings, or else due 
to the logging operations themselves. The results forecasted in this way 
must be invariably too high. 

Pinchot's Spruce Tables (The Adirondack Spruce, p. 77) are based on 
similar premises : 

a. Construct volume tables by stem analysis (stump-analysis) on land 
cut over for a second time, thus showing rate of growth for trees left 
standing at the first cut. 

b. Construct tables, by actual measurements in the woods, giving the 



6 4 



Forest Mensuration 



number of trees of the various diameters, composing a stumpage of from 
1,000 to 12,000 feet board measure. 

c. Predict the number of trees and their exact diameters to be found 
10, 20 or 30 years after logging, according to severity of logging (diam- 
eter limit). 

d. With the help of the volume tables, give the contents of these trees. 

In these tables as well, the death rate amongst trees is disregarded. For 
normal death rate, compare Pinchot's "White Pine," p. 80, ff; also remarks 
at end of Paragraph LIV. 



PARAGRAPH XCVII. 



THE INCREMENT OF A W00DL0T. 



The current as well as the annual average increment of normal, even- 
aged woods culminates at a much earlier date than the increment of the 
trees composing such woods. The explanation lies in the death rate of 
the trees. 

Under a close crown density in even-aged, normal woods, the stronger 
half of the trees yield, from the pole stage on, practically all the incre- 
ment, the weaker half of the trees being almost inactive. 

The better the quality of the soil, the earlier occurs the culmination of 
the increment; consequently, on good soil, shorter rotations are apt to be 
advisable than on poor soil. 

Light demanding (intolerant) species show an earlier culmination than 
shade bearers (tolerant) species. 

For white pine woods, after Pinchot, the years of increment culmina- 
tion are as follows : 



Culmination 


For entire volume with 
bark in cu. ft. 


For volume Doyle in 
ft. b. m. 


of 


I. 


II. 


III. 


I. 


II. 


III. 


Current inert.. . . 
Average inert . . . 


40th 
60th 


50th 
80th 


60th yr. 
1 ooth yr. 


70th 
i35th 


70th 
1 60th 


noth yr. 
210th yr. 



I denotes best; II denotes medium, and III denotes poorest quality of 
soil. 

The increment of a woodlot, whether normal or abnormal, can be 
obtained : 

a. With the help of yield tables. 

b. By special investigations made into the rate of growth of sample 
trees (Paragraph XCVIII.). 



Forest Mensuration 65 

c. With the help of the average annual increment of the woodlot (Par- 
agraph XCIX.)- 

The increment of a past period is never exactly equal to that of a 
future period, unless the age of the woods is close to that year at which 
the increment culminates. The increment percentage during a past period 
is always larger than the increment percentage during a coming period 
(aside of temporary increase due to light-increment). 

The general laws (Paragraph LXXV.) relative to the culmination, 
increase and decrease of increment hold good for the volume increment 
of woodlots as well as for that of trees. 



PARAGRAPH XCVIII. 

ASCERTAINING THE INCREMENT OF WOODLOTS BY SAMPLE TREES. 

The current annual volume increment and the volume increment per- 
centage of a wood, from which its maturity largely depends, can be cor- 
rectly found only by a valuation survey, combined with an investigation 
into the present rate of growth exhibited by a number of sample trees. 

Borggreve recommends to gauge the increment of the sample trees by 
the Schneider increment percentage. This is usually insufficient. 

The correct volume increment percentage p of a woodlot is obtained 
from the volume increment percentage pi, pn, p3, p< and ps of the class sam- 
ple trees — which represent class-volumes vi, vj, vs, V4 and x- — as 

v i Pi + v j P 2 4- v 3 p 3 + v 4 p 4 + v 5 p 5 



V l + V 2 4" V 3 + V 4 + V 5 

Where the form heights of the classes differ slightly only, the sectional 
areas of the classes may be substituted for the volumes of the classes. 

Again, where classes of equal sectional area are formed (after Robert 
Hartig), there the volume increment per cent, of the woodlot equals the 
arithmetic mean of the volume increment percentages of the sample 
trees, so that 

Pi +P2 + Ps + P4 + P5 



PARAGRAPH XCIX. 

CURRENT INCREMENT ASCERTAINED FROM AVERAGE INCREMENT. 

Within certain limits, a short time previous and a short time after the 
culmination of the average annual increment, the annual average incre- 
ment equals the current increment and can be used in its place as a basis 
for yield calculation. European Governments frequently prescribe this 
modus operandi for yield forecasts in working plans. 



66 Forest Mensuration 

CHAPTER IV.— LUMBER 

PARAGRAPH C. 

UNITS OF LUMBER MEASUREMENT. 

For rough lumber one inch thick, or thicker, the unit of measure, known 
as one foot board measure, is a square foot of lumber one inch thick. 
*" v ^~""*- (,"i^)This unit is the i/i2th part of a cubic foot. 

■ For rough lumber thinner than one inch, the unit of measure, also 
-, $ known as one foot board measure, is the superficial square foot, and the 
thickness of the lumber is here entirely disregarded. 

All dressed stock is measured and described as if it were the full size 
of the rough lumber necessarily used in its manufacture. "Inch flooring," 
e. g., is actually 13/16 inch thick ; and "^ inch ceiling" is actually 5/16 
inch thick. 




Standard thicknesses are: 

tff » J • h -' 8 ' *' J > I i' x 2' 2 ' 2 2> 3 x 4 • 

Standard lengths are: 

in hardwoods 6 to 16 feet; 

in softwoods 10 to 24 feet. 
In both cases, lengths in even feet (not in odd feet) are required. 
A shortness of 1" or 2" in the length of hardwood boards is disregarded. 

Standard defects are : 

I. In hardwoods: one sound knot of 1 \" diameter; 

one inch of bright sap ; ► 

one split, its length in inches equalling the contents of 
the board in feet b.m. 

II. In softwoods : sound knots, viz. : 

(a) pin-knots of not over J" diameter; 

(b) standard knots of not over ij" diameter ; 

(c) large knots of over i\" diameter; 

pitchpockets, viz. : 

(a) small pitchpockets J" wide; 

(b) standard pitchpockets up to |" wide and up to 3' 
long; 

pitchstreaks, viz. : 

(a) small pitchstreaks not wider than j l 5 the width and 
not longer than }■ the length of board ; 

(b) standard pitchstreaks with dimensions up to twice 
as large as given under (a); 

sap, viz..: 

(a) bright sap ; 

(b) blued sap ; 

splits, wane, scant width, tongues, less than y\" long. 



Forest Mensuration 67 

The point at which a defect is located greatly influences its effect on 
the grade of the lumber. 

The two faces, the two edges and the two ends of a board must be 
parallel. In case of unevenness, the thinnest thickness, the narrowest 
width and the shortest length are measured. 

Lumber is measured with the help of a lumber rule (Lufkin rule) which 
yields for inch boards of given lengths and given width the correspond- 
ing contents in feet b. m. 

In measuring the widths, fractions of an inch are neglected in rough 
lumber. 



PARAGRAPH CI. 

INSPECTION RULES AND NOMENCLATURE. 

The lumber inspection prevailing in a given market is governed by 
local custom or by agreement within the body of local associations of 
lumbermen. 

The tendency of all inspection rules is directed toward a gradual lower- 
ing of rigidity. 

The wholesaler's inspection is generally stiffer than that of the manu- 
facturer. Diversity of rules is a sadly demoralizing element in lumber 
circles. 

Lumber sawn for special purposes {e. g., wagon bolsters) must be in- 
spected with a view to its adaptability for such special purpose. 

A. Hardwood. The grade of a board depends on 

1. Its width and length; 

2. Its standard defects ; 

3. The percentage of clear stock contained therein ; 

4. The number of cuttings yielding such clear stock. 

The following table shows average specifications prevailing for the 
various grades of hardwood lumber in the U. S. markets. 

The defects specified invariably indicate the coarsest stock admissible 
in a given grade. 



68 



Forest Mensuration 









Hardwood 


Lumber Specifications. 




Designation 


Minimum 


Actual 


Allows of 


of 
Grade. 


Len'h 
feet. 


Wi'th 

inch- 
es. 


Length 
feet. 


Width 
inches. 


No. of 
standard 
defects. 


Rate 
of clear 
stock. 


Con'd in 
c't'ngsnot 
more than 


Firsts 

Seconds 


IO 

8 

IO 


8 
8 
6 


i o & over 
i o & over 

8 

8 
i o & over 
io & over 
i o & over 
io & over 


8&9 
io & over 

8&9 
io & over 

6& 7 

8&9 

IO & II 

1 2 & over 


none 
one 
none 
one 
none 
one 
two 
three 


"3 

a 
u 


V 

a 

o 

o 

In 

Ph 


No. i Com... 


6 

8 


6 

4 


6 
6 
8 
8 
8& io 

12 to 1 6 


6 to 8 
9 & over 

4 

5 
6 & over 
6 & over 


none 
one 
none 
one 


all 
all 
all 
all 

§ 


I 
I 

I 
I 

2 

3 


No. 2 Com.. . 


6 


3 


6 to io 
12 to 1 6 






i 


3 
4 














No. 3 Com.. . 


4 


3 








\ 













B. Softwoods. Softwood lumber is inspected from its best side 
Under "edgegrain" is understood lumber the face of which forms an* angle 
of less than 45 degrees with the plain of the medullary rays contained in 
the board. All other lumber is termed "flat grain" or "slash grain," also 
"bastard grain." 



I. Finishi?ig Lumber, 1" to 2" thick, dressed one or two sides. 

1. First and second clear, 

up to 8" wide ; absolutely clear ; 
10" wide; one small defect permitted; 

12" and over wide; \ of stock may have one standard knot or 
its equivalent. 

2. Third clear, 

allows of twice as many defects. 

II. Flooring, 1" thick and 3" or 4" or 6" wide before dressing; either 
with hollow back or with solid back ; 

1. A, B and C flat grain flooring ; wherein "A" is clear and "B" al- 

lows of one or two standard defects ; 

2. A, B and C edgegrain flooring ; with the same allowance ; 

3. No. 1 and No. 2 fence flooring. 



Forest Mensuration 69 

III. Ceiling, f, $ and | inch thick; 3, or 4, or 6 inches wide. 

1. "A" ceiling and "B" ceiling, with small defects only; 

2. No. 1 and No. 2 common ceiling, with one and two standard de- 

fects, or their equivalent. 

IV. Drop Siding, which is either "shiplapped" or "tongued and grooved;" 

it is %" thick and 3^ or 5J inches wide. Grades A, B and No. 1 
common. 

V. Bevel Siding, which scales T y at the thin edge and \" at the thick 
edge, resawn from stock dressed to £$" x 5$". Grades as under IV. 

VI. Partition, measuring f " x 3J" or |" x 5I". Grades as under IV. 

VII. Common Boards, graded as No. 1, No. 2 and No. 3 common boards, 
8", 10" or 12" wide, dressed one or two sides, or rough. 

VIII. Fencing, graded as No. 1, No. 2 and No. 3 fencing, 3", 4" or 6" wide. 
The grade "No. 3" includes defective lumber with knot-holes, red 
rot, very wormy patches, etc., on \ of the length of the board. 
Fencing is either dressed or rough. 



CHAPTER V.— STUMPAGE VALUES 

PARAGRAPH CII. 

STUMPAGE VALUES. 

Forestry is a business ; the forest largely represents its business invest- 
ment ; its purpose is the raising of money, of dividends. 

Thus it is with investments and the dividends therefrom that the fores- 
ter is concerned; and it is the task of "forest finance" and "forest manage- 
ment" to ascertain the factors and to regulate the components of such 
investments. 

Forest mensuration, as a subsidiary to forest management, may well 
devote a chapter to the measurement of the stumpage value of trees. 

Stumpage value is the price which a tree brings or should bring if it 
were sold on the stump. 

The stumpage-value of a tree depends on the value of the lumber con- 
tained therein and obtained therefrom, deducting the total expense of 
lumber production (logging, milling, shipping, incidentals.) 

Since the value of lumber fluctuates, as well as the cost of production, 
stumpage values are subject to continuous variation. The tendency of 
stumpage prices, all over the world, is a tendency to rise — especially so 
in countries of rapid development, rapid increase of population and in- 
adequate provisions for re-growth. 



70 Forest Mensuration 

The cost of production is composed about as follows : 

i. Expense of logging and log transportation, varying locally be- 
tween $2 and $5 per i,ooo' b. m. 

2. Expense of milling, varying between $1.50 and $5 per 1,000' b. m. 

3. Expense of freightage of lumber to the consuming market, 

amounting per 1,000' b. m. to $1.50 for very short hauls; to 
$12 for a haul from Atlanta to Boston; to $21 for a haul across 
the continent from Portland (Oregon) to New England. 

Freight rates have, in the long run, a decided downward tendency. 
Still, with a majority of the lumber produced in the U. S., the item 
"freight" forms the chief expense of production. 

For Pisgah Forest a reduction of freight rates equalling 1 cent per 100 
lbs. involves a net gain for the owner of approximately $60,000. In this 
possibility lies one of the strongest arguments for conservative lumbering. 

An increase of the price of lumber from $20 to $21 at the place of con- 
sumption endears the lumber to the consumer by 5% ; the owner of the 
forest now valuing his stumpage at $5 will eventually experience this in- 
crease as a 20% increase of stumpage values. 

The only factors of stumpage-values, which the owner himself — unaided 
by the development of the country — may influence, consist in the expense 
of logging and log freighting, and in the expense of milling, the former 
largely depending on the quality of available means of transportation, the 
latter governed by the quality of the sawmill. 

In ascertaining the stumpage-value of a tree the forester considers : 

a. The cost per 1,000' b. m. of logging it, of milling it and of freight- 

ing its timber; 

b. The volume of timber contained in the tree, by grades ; 

c. The value of such lumber, by grades. 

If a tree contains 
45% of lumber worth $31 per 1,000' b. m. 

It is necessary to find Stoetzer's constant factor of increment or to 
ascertain the relative increment of the sectional areas of the sample trees 
at 0.45 of their heights. 

35% of lumber worth $21 per 1,000' b. m. 

15% of lumber worth $16 per 1,000' b. m. 

5% of lumber worth $8 per 1,000' b. m. 

then, the lumber value of the tree, per 1,000' b. m., is 

45 x 31 + 35 x 21 + 15 x if, + 5 x 8 



100 



= $24.10 



Deducting from this figure the expense of logging, milling and freight- 
ing, the actual stumpage-value, per 1,000' b. m., is derived. 

The actual prices paid for stumpage in the U. S. fall deeply below the 
figures which a test-calculation is apt to yield. 



Forest Mensuration 



71 



This discrepancy may be explained, above all, by 

Ignorance of owners of stumpage ; 
Agents' and dealers' profits ; 
Incidental expenses overlooked. 

Stumpage-values show a rapid decrease with the increase of the dis- 
tance separating the tree from the nearest railroad or stream. 

The grades of lumber and their proportion obtainable from logs of 
given species, diameter and soundness (including presence and location 
of defects) can be ascertained only by test-sawing in the mill. 

This has been done in 1896 for yellow poplar at Biltmore (bandsaw 
mill). The stumpage-values then ascertained are shown by the follow- 
ing table : 

Market Value of Poplar Stumpage in Western North Carolina, Per 

Tree, in Cents. 



<*-! 


Under good 




Jnder average 




Under poor 


O 

4> 


conditions. 




conditions. 




conditions. 


be 




Logging and Milling 




Logging and Milling 




Logging and Milling 


<u b 


. ui 


expenses being per 


■ t/j 


expenses being per 


• in 


expenses being per 


5 & 


H_= 
n 


1000 feet B. M. 


Eg 


1000 feet B. M. 


.So 


1000 feet B. M. 














< 


S-S 


$9 


Sio 


$n 


O.S 


$9 


$10 $11 


P.S 


$9 Sio 


$11 


IOo 




Nega- 


Nega- 


Nega- 




Nega- 


Nega- Nega- 




Nega- Nega- 


Nega- 






tive. 


tive. 


tive. 




tive. 


tive. 


tive. 




tive. 


tive. 


tive. 


I20 


18.8 


8 


« 


«. 




« 


<< 


« 




« 


■ < 


« 


140 


21 .3 


40 


25 


" 


18 


2 


4 


" 


" 






" 


" 


" 


160 


23-5 


105 


7 2 


2 


20 


4 


22 


5 


" 






" 


" 


" 


i So 


25-7 


265 


170 


98 


2 2 


4 


67 


35 


" 






" 


" 


" 


200 


27.7 


445 


325 


23O 


24 


3 


160 


103 


3D 


18 


5 


" 


" 


" 


220 


29.6 


620 


465 


350 


2h 





287 


200 


109 


20 


O 


7 


" 


" 


240 










27 


5 


430 


330 


210 


21 


3 


27 


3 


" 


260 
















460 


330 


22 


1 


60 


25 


" 


280 


























45 


" 


300 




























5 


320 




























30 



Footnote : Dots below a column of figures indicate higher values, not 
specifically ascertained. 

The values above the columns of figures are all negative and were not 
ascertained specifically either. 



It is to be hoped that similar tests will be made for our leading species 
on a large scale by the U. S. Forest Service or by the various associations 
of lumber manufacturers. Conservative forestry as a business badly re- 
quires data allowing to estimate the actual value of logs, and hence of 
trees, if the uncertainty of financial results now checking the progress of 
conservative forestry in America is to be definitely reduced. 







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